# Chapter 8. Chapter 8 Opener. Section 8.1. Big Ideas Math Green Worked-Out Solutions. Try It Yourself (p. 353) Number of cubes: 7

Save this PDF as:

Size: px
Start display at page:

Download "Chapter 8. Chapter 8 Opener. Section 8.1. Big Ideas Math Green Worked-Out Solutions. Try It Yourself (p. 353) Number of cubes: 7"

## Transcription

1 Chapter 8 Opener Try It Yourself (p. 5). The figure is a square.. The figure is a rectangle.. The figure is a trapezoid. g. Number cubes: 7. a. Sample answer: 4. There are unit cubes in each layer. Because there are layers, there are 0 90 unit cubes in the prism. So, the volume is 90 cubic units. 5. There are unit cubes in each layer. Because there are 6 layers, there are unit cubes in the prism. So, the volume is 0 cubic units. b. Sample answers: 6. There are 8 4 unit cubes in each layer. Because there are 4 layers, there are unit cubes in the prism. So, the volume is 96 cubic units. Section Activity (pp ). b. Number cubes: 4 c. Number cubes: 4 d. Number cubes: 5 e.. a. The red shape is a face. The blue line segment is an edge. The green point is a vertex; Sample answer: A face is a flat surface prism. An edge is a length face. A vertex is a point where edges meet. b. There are 6 faces, edges, and 8 vertices. c. The dots represent the vertices. To draw the edges, connect two dots. To draw the faces, connect at least dots forming a closed figure. d. Sample answer: Planes are parallel if they never intersect; lines are parallel in if they lie on the same plane and do not intersect; a line is parallel to a plane if they never intersect; lines are perpendicular if they meet at a right angle; planes are perpendicular if they meet at a right angle; a line is perpendicular to a plane if they meet at a right angle. d e f A B Number cubes: 6 f. Number cubes: 0 C Faces A and B are parallel. Face C is perpendicular to faces A and B. Edges d and e are parallel. Edge f is perpendicular to edges d and e. Edges d and e are parallel to face C. Edges d and e are perpendicular to faces A and B. 9

2 4. Sample answer: You can use dot paper to draw threedimensional figures formed by cubes by shading parallel s the same color to create a three-dimensional illusion. 8. On Your Own (pp ). The solid has face on the, faces on the s, and face each on the and. The faces intersect at 9 different line segments. The edges intersect at 6 different points. So, the solid has 5 faces, 9 edges, and 6 vertices The statement is false. Some the edges rectangular prism are perpendicular and some are neither (skew). 6. The statement is false. Opposite edges the base are parallel. Practice and Problem Solving Number cubes: 0 Number cubes: 9 4. : The view is a triangle. 9. : : The view is a rectangle. The view is a rectangle. Number cubes: 9 0. The solid has face on the, face on the, and 5 faces on the s. The faces intersect at 5 different line segments. The edges intersect at 0 different points. So, the solid has 7 faces, 5 edges, and 0 vertices. 5. : The view is a triangle.. The solid has face on the, face on the, and 8 faces on the s. The faces intersect at 4 different line segments. The edges intersect at 6 different points. So, the solid has 0 faces, 4 edges, and 6 vertices. : : The view is a triangle. The view is a square.. The solid has face on the and 6 faces on the s. The faces intersect at different line segments. The edges intersect at 7 different points. So, the solid has 7 faces, edges, and 7 vertices Exercises (pp ) Vocabulary and Concept Check. The statement is false. A triangular prism has two triangular faces The statement is true.. The statement is true. 4. The statement is false. A rectangular pyramid has four triangular faces. 40

3 7.. The view is a triangle. The view is a rectangle. The view is a rectangle. 4. The Washington Monument is an obelisk. It consists pyramid sitting on solid that tapers as it rises The view is a triangle. The view is a triangle. The view is a triangle. The view is a rectangle. The view is a rectangle. The view is a triangle. 7. Answer should include, but is not limited to: an original drawing house; a description ny solids that make up any part the house. 8. a. The greatest number cubes is 9. b. The least number cubes is 5. c. (a): (b): Sample answer: 0. The view is a rectangle. The view is a hexagon. The view is a rectangle The view is a rectangle. The view is a rectangle. The view is a hexagon. The view is a rectangle. The view is a trapezoid. The view is a rectangle. 9. Sample answer: a. Triangular prism Square pyramid Vertices: 6 Vertices: 5 Edges: 9 Edges: 8 b. More than one solid can have the same number faces, so knowing the number edges and vertices can assist you in drawing the intended solid. Fair Game Review 0. A bh ( 7)( 4) 8 The area is 8 square meters. 8 The area is square centimeters.. A bh ()() The area is 5 square feet.. A ( b b) h ( )( ). D; Because y and x, the statement y > x is true. 4

4 Section Activity (pp. 60 6). a. Sample answer: Working from to, the first blank is the base and the second blank is the lateral face. The prism identified by the base is rectangular. b. Sample answer: Working from to, the first blank is the base and the second blank is the lateral face. The prism identified by the base is triangular.. a. Check students work. b. The figure should be similar to the one in the book. The prism formed is a rectangular prism.. a. Lateral Face Base Lateral Face Base Lateral face areas: Base areas: entire surface: square units b. Base Net Lateral Face Net Lateral Face b. Lateral face areas: Base areas: entire surface: 84 square units 5. Sample answer: You can draw a two-dimensional representation the prism by first finding the area each face, and then finding the sum the areas. 8. On Your Own (pp. 6 6). Use a net to find the area each face. Top: Bottom: Front: Back: Side: Side: m Lateral Face Lateral Face Lateral Face 6 m 6 m 6 m 9 m Base 5 m 4. a. Lateral face areas: Base areas: entire surface: 88 square units S So, the surface area is 58 square meters. Lateral face areas: Base areas: entire surface: 78 square units 4

5 . Use a net to find the area each face. Top: Bottom: Front: 5 6 Back: 5 6 Side: 5 6 Side: in.. Use a net to find the area each face. Top: Bottom: Front: Back: Side: Side: ft 8 ft 0 ft 0 ft 8 ft. 5 in. 5 in. 5 in. 5 in. S So, the surface area is 80 square inches. 6 in. + So, the surface area is 80 square inches. 4. Use a net to find the area each face. Bottom: Front: 4 6 S Back: 4 6 Side: Side: 4 yd 4 yd 4 yd 5 yd 5 yd So, the surface area is 60 square yards. S

6 5. Use a net to find the area each face. Bottom: Front: Back: Side: Side: m 6 m 6 m 6 m So, the surface area is 40 square meters. 6. Use a net to find the area each face. Bottom: Front: Back: Side: Side: m 9 m S Exercises (pp ) Vocabulary and Concept Check. Find the sum the areas the faces.. The statement that is different is "What is the area the triangular faces the prism?". What is the area the triangular faces the prism? A b h Because there are triangular faces, multiply the above answer by. So, 4 48 square feet. What is the surface area the prism? Use a net to find the area each face. Bottom: Front: Back: Side: Side: ft 0 ft 6 ft 8 ft 8 ft 7 ft 6. ft 8.6 ft 7.6 ft 7.6 ft 6. ft 0. ft So, the surface area is 6 square feet. S So, the surface area is 99. square feet. S

7 Practice and Problem Solving. 6. Use a net to find the area each face. Top: Bottom: Front: 0 0 Back: 0 0 Side: 5 5 Side: ft Lateral face areas: Base areas: entire surface: square units 0 ft ft 4. S So, the surface area is 0 square feet. 5. Lateral face areas: Base areas: entire surface: square units 7. Use a net to find the area each face. Top: Bottom: Front: 6 8 Back: 6 8 Side: 9 7 Side: cm 9 cm 9 cm 9 cm 6 cm cm Lateral face areas: Base areas: entire surface: square units S So, the surface area is 98 square centimeters. 45

8 8. Use a net to find the area each face. Top: 4 8 Bottom: 4 8 Front: 5 0 Back: 5 0 Side: Side: yd 0. Use a net to find the area each face. Bottom: Front: Back: Side: Side: yd 7 m 5 m 7 m 4 yd 4 yd yd 7 m 6 m 7 m 0 m 5 yd S S So, the surface area is 740 square meters.. Use a net to find the area each face. Top: So, the surface area is 76 square yards. 9. Use a net to find the area each face. Bottom:. 6.6 Front: Back: Side: 6 Side: ft ft. ft ft ft Bottom: Back: Side: 4 Side: 4 4 mm 4 mm 5.7 mm 4 mm mm ft S So, the surface area is 57. square millimeters. S So, the surface area is 7.6 square feet. 46

9 . The least amount wrapping paper needed to wrap the gift box is equal to the surface area the gift box. Use a net to find the area each face. Top: Bottom: Front: Back: Side: Side: in. 8 in. 8 in. 8 in. 8 in.. The least amount fabric needed to make the tent is equal to the surface area the tent. Use a net to find the area each face. Front: 6 4 Back: 6 4 Bottom: Side: Side: ft 4 ft 0 in. 7 ft S So, the least amount wrapping paper needed to wrap the gift box is 448 square inches. S So, the least amount fabric needed to make the tent is 6 square feet. 4. Use a net to find the area each face. Bottom: Front: Back: Side: Side: ft... 6 ft 6 ft S So, the surface area is 8 square feet, which is the amount glass used. 47

10 5. area Box : Use a net to find the area each face. Top: Bottom: Front: Back: Side: Side: in. 6 in. 6 in. 6 in. So, Box has a surface area 448 square inches. Use the relationship foot inches to find the number square inches in one square foot. ft ft ft in. in. 44 in. area in square feet: ft S 448 in. 44 in. Cost to make 50 Box : 9 ft 0 in. C \$.5 50 ft \$ ft area Box : Use a net to find the area each face. Top: Bottom: Front: Back: Side: 4 8 Side: in. S in. 4 in. 4 in. 4 in. 5 in. 8 in. So, Box has a surface area 44 square inches. area in square feet: S ft 7 44 in. 8 Cost to make 50 Box : 44 in. ft 7 \$.5 C 50 ft \$ ft Difference Box and Box : C C \$94.44 \$84.0 \$0.4 So, the company will save \$0.4 by choosing to make 50 Box instead 50 Box. 6. Use a net to find the area each face to be stained. Front: Back: Side: Side: 5 0 To Be Painted S in. ft 5 0 So, the surface area the part the ramp to be stained is 87 square feet. Because one quart stain covers 00 square feet and quarts, you should buy quarts stain to cover the ramp. S

11 7. Find the surface area the rectangular prism before removing the cube. area rectangular prism before removing cube: Use a net to find the area each face. Top: Bottom: Front: Back: Side: Side: ft 8 ft area rectangular prism before removing cube cube cube cube cube cube cube 8 ft 8 ft 9 ft S So, the surface area the figure after removing the cube is 64 square feet. So, the surface area before removing the cube is 4 square feet. Use a net to find the area each face the cube. Top: Bottom: Front: Back: Side: Side: S Fair Game Review 8. A bh ()(8) The area the triangle is 48 square meters. A bh ()(5) 65 The area the triangle is 65 square feet. 0. A bh (0)() 5 Subtract the areas the and the cube from the surface area the rectangular prism before removing the cube and add the areas the,, and s the cube. The area the triangle is 5 square inches.. C; x ? So, x 4 is not a solution. 49

12 Study Help Available at BigIdeasMath.com. Quiz The solid has face on the, face on the, and 4 faces on the s. The faces intersect at different line segments. The edges intersect at 8 different points. So, the solid has 6 faces, edges, and 8 vertices. 7. Use a net to find the area each face. Top: ()() 4 6 Bottom: ()() 4 6 Front: Side: 0 0 Side: cm 4 cm. The solid has face on the and faces on the s. The faces intersect at 6 different line segments. The edges intersect at 4 different points. So, the solid has 4 faces, 6 edges, and 4 vertices. 0 cm. cm 4 cm 4. S So, the surface area is square centimeters. 8. Use a net to find the area each face. Top: 4 8 Bottom: 4 8 Front: 4 Back: 4 Side: 6 Side: 6 4 in. 5. in. in. in. 4 in. in. 6. S So, the surface area is 5 square inches. 50

13 9. a. Use a net to find the area each face. Top: Bottom: Front: 9 08 Back: 9 08 Side: 4 48 Side: in. 4 in. 4 in. 4 in. 9 in. in. b. After the manufacturer reduces each the dimensions by inch, the cereal box has a length 8 inches, a width inches, and a height inches. Use a net to find the area each face. Top: 8 4 Bottom: 8 4 Front: 8 88 Back: 8 88 Side: Side: 8 in. in. in. in. 8 in. in. S So, the surface area the cereal box is 84 square inches. S The surface area the cereal box after the manufacturer reduces each the dimensions by inch is 90 square inches. So, the decrease in surface area is square inches. 5

14 0. Use a net to find the area each face. Bottom: Front: Back: Side: Side: cm lateral face lateral face base lateral face 6.5 cm 6.5 cm 5 cm S cm 6 cm Sample answer: lateral faces: Base area: entire surface: The surface area the triangular pyramid is 69 square units. 4. a. So, the surface area the gift box is 90 square centimeters. Section Activity (pp ). a. Working from to, the first face is a lateral face and the second face is the base. The pyramid is a rectangular pyramid because the base is a rectangle. b. Working from to, the first face is a lateral face and the second face is the base. The pyramid is a triangular pyramid because the base is a triangle.. a. Check students' work. b. The pyramid should look like the pyramid in the book. The base is a square. So, the pyramid is called a square pyramid. c. lateral faces: Base area: entire surface: So, the area the square pyramid is square units. lateral faces: Base area: 9 entire surface: The surface area the square pyramid is square units. b. 5 lateral faces: Base area: entire surface: The surface area the square pyramid is 75 square units.

15 5. Find the sum the areas the faces shown by the net. 6. Sample answer: The lateral faces are identical, so their areas are the same; The bases and heights the triangular lateral faces will have the same measure, so they are identical and have the same area. 8. On Your Own (pp. 70 7). Use a net to find the area each face. Bottom: 4 Side: Side:. Use a net to find the area each face. Bottom: Side: Side: Side: Side: cm 5 cm 5 cm Side: Side: ft ft ft S So, the surface area is 75 square centimeters. So, the surface area is 6 square feet. S Use a net to find the area each face. Bottom: Side: Side: Side: Side: in..6 in. 4 in. So, the surface area is 44.8 square inches. S

16 4. Use a net to find the area each face. Bottom:.7.7 Side: Side: Side: 6. Use a net to find the area each face. Bottom: Side: 0 0 Side: 0 0 Side: yd cm cm.7 cm yd 7. yd So, the surface area is 0.7 square centimeters. 5. Use a net to find the area each face. Bottom: Side: Side: S So, the surface area is 5 square yards. 8. Exercises (pp. 7 7) S Vocabulary and Concept Check. First draw a net the pyramid to find the area the each face. Then find the sum the areas the faces.. The third figure; The third figure is a prism, not a pyramid like the other three figures. Side: in. 7.8 in. 7 in. S So, the surface area is 9.6 square inches. 54

17 Practice and Problem Solving. 5. lateral faces: base: 9 entire surface: The surface area the figure is 7 square units. 4. lateral faces: base: entire surface: The surface area the figure is 60 square units. 6. Use a net to find the area each face. Bottom: Side: Side: Side: Side: in. 5 in. lateral faces: base: entire surface: The surface area the figure is 65 square units. S So, the surface area is 9 square inches. 55

18 7. Use a net to find the area each face. Bottom: Side: Side: Side: Use a net to find the area each face. Bottom: 44 Side: 7 0 Side: 7 0 Side: 7 0 Side: Side: 7 0 cm 7 cm 6 yd.4 yd S So, the surface area is 7.8 square yards. S So, the surface area is 55 square centimeters. 9. Use a net to find the area each face. Bottom: Side: 9 54 Side: 9 54 Side: ft ft 0.4 ft S So, the surface area is 4.4 square feet. 56

19 0. Use a net to find the area each face. Bottom: Side: Side: Side: Use a net to find the area each face. Bottom: Side: Side: Side: in. 6.9 in. 8 m 4 m.5 m 4 in. S So, the surface area is 95.6 square inches. So, the surface area is 55 square meters.. Use a net to find the area each face. Bottom:.7.7 S Side:.. Side:.. Side:... in. in..7 in. S So, the surface area the paperweight is 7.7 square inches. 57

20 . Use a net to find the area each triangular face. 5. Use a net to find the area each face. Bottom: ft 6 ft 9.7 ft Side: Side: Side: 6 x x Side: 6 x x Side: 6 x x Side: 6 x x 6 in. x Side: in. Side: Triangular Faces So, the surface area the 4 triangular faces the entrance the Louvre Museum is,74.4 square feet. 4. Use a net to find the area each face. Side: Side: Side: Side: S ,74.4 ft ft ft The value x is 4 inches x + x + x + x x 48 x 4 x S So, the surface area the light cover is 8 square feet. The weight the cover is pounds. Yes, the chain can support the light cover because the weight the glass is 9.6 pounds, which is less than the limit 5 pounds for the chain. 58

21 6. The area the base is 6 times the area triangle with a base 8 centimeters and a height 6.9 centimeters. base: cm Use a net to find the area each face the pyramid. Bottom: no; When you fold the net below, the four triangles will lie flat on the square. D A 4 in. 4 in. 7 in. B 7 in. Fold 4 in. 7 in. A D 4 in. B 7 in. C Side: 8 5 C 7 in. Side: 8 5 Side: 8 5 Side: 8 5 Side: 8 5 Also, when you lift up the folded triangles above, they will not touch. So, they do not form a pyramid. Fair Game Review 8. Frogs Turtles 6 The equivalent ratios are: 7 to, 4 to 6, and 8 to. Side: Apples Oranges 4 The equivalent ratios are: 0 to 4, 5 to, and 0 to. 66. cm 8 cm cm 0. B; Quadrant II ( 7, ) O (, ) Quadrant III y Quadrant I (, 4) x (5, ) Quadrant IV S The point (, ) is in the third quadrant. So, the surface area the hexagonal pyramid is 478. square centimeters. 59

22 Section Activity (pp ). a. 4 unit unit. a. As indicated by the denominators the dimensions, divide the parallel edges unit cube into (length), (width), and 4 (height) equal parts, find the volume one the resulting identical prisms, find how many it takes to fill the rectangular prism, multiply to find the volume. equal parts unit b. The fraction the volume the unit cube that one these identical prisms represents is. 4 4 equal parts The volume one the identical prisms is 4 cubic units. Twenty-four identical prisms make up the unit cube, so one represents the volume. The volume 4 the unit cube is cubic unit, so the volume one the identical prisms is cubic unit. 4. a. It takes 8 identical prisms from Activity (a) to fill the rectangular prism. 4 unit 4 unit unit unit unit m m 4 m 4 m equal parts There are 6 the identical prisms shown to the left in a -meter cube, so the volume each is cubic meter. 6 There are these in the rectangular prism. units b. Each identical prism has an area cubic unit and 4 it takes 8 them to fill the rectangular prism. 8 8, or cubic unit m m So, the volume the rectangular prism is cubic meter

23 b. As indicated by the denominators the dimensions, divide the parallel edges unit cube into (length), 4 (width), and 5 (height) equal parts, find the volume one the resulting identical prisms, find how many it takes to fill the rectangular prism, multiply to find the volume. equal parts 5 equal parts 4. yes; Sample answer: The formulas work for the prisms in Activities and. Example from Activity a: V wh 4 cubic meter 6 Example from Activity b: V wh , or cubic inch 60 5 in. 5 in. 4 in. 4 equal parts There are 60 the identical prisms shown to the left in a -inch cube. So, the volume each is cubic inch Sample answer: Fill the prism using identical prisms with unit fraction edge lengths for which you know the volume, count the number prisms needed, and multiply to find the volume; or use the formula V bh or V wh. 8.4 On Your Own (pp ). V wh So, the volume is cubic foot. 4 in. 4 in. There are 48 these in the rectangular prism. So, the volume the rectangular prism is 48 48, or 4 cubic inch in.. V wh So, the volume is 7 64 cubic yard.. V wh 0() So, the dump truck can haul 760 cubic feet dirt when it 70 lb is full. To find the weight the dirt, multiply by. ft 760 ft 70 lb 5,00 lb ft The dump truck can haul about 5,00 pounds dirt when it is full. 6

24 4. 5. V wh ( )( ) The length is 6 inches. V wh 75 0( w) w 75 0w 0 0 w The width is centimeters.. The question that is different is "How much does it take to cover the rectangular prism?" This question asks for the surface area the rectangular prism. The other three questions ask for the volume the rectangular prism. Use a net to find the area each face. Top: Bottom: Front: Back: Side: Side: cm 7 cm 7 cm 7 cm 5 cm 8.4 Exercises (pp ) 0 cm Vocabulary and Concept Check. The volume n object is the amount space it occupies. The surface area n object is the sum the areas ll its faces.. yes; You just substitute the decimal edge lengths into the formula and multiply. S So, the surface area is 0 square centimeters. V wh 57 ( )( 0) 50 So, the volume is 50 cubic centimeters. Practice and Problem Solving 4. V wh So, the volume is 0 cubic inch. 6

25 V wh 7 4 5, or 6 6 So, the volume is 5, or 6 6 V wh So, the volume is 8 5 V wh ( ) So, the volume is 5 6 V wh cubic foot. cubic meter. cubic centimeters. So, the volume is 8 cubic centimeters. V wh So, the volume is cubic meters. V wh ( ) h 60 8h 60 8h h So, the height is 0 centimeters... V wh ( w)( ) w w w So, the width is 4.5 centimeters. V wh 5 9( w) 4 5.5w 5.5w w So, the width is 6 inches.. V wh ()( ) The volume the water in the tank when it is full is.75 cubic feet. The weight the water is pounds. So, the fish tank can hold 4 pounds water when it is full. 4. The layer is centimeters long and centimeters wide and made up -centimeter cubes. So, you need to divide by 4 4 to determine the length and width the cube, which is 6. So, you need6 6, or 56 cubes to cover the the cube. To fill the cube, you need 6 layers 56 cubes. So, you need cubes to create a cube with an edge length centimeters. 5. The layer is cubes long ( inches foot) and cubes wide. So, you need, or 44 cubes to cover the the cube. To fill the cube, you need layers 44 cubes. So, you need cubes to create a cube with an edge length inches, or foot. There are 78 -inch cubes in a cube with an edge length foot. The volume the cube with an edge length foot is cubic foot, or 78 cubic inches. So, cubic foot is equal to 78 cubic inches. You can use 78 in. ft the conversion factors and to convert ft 78 in. between cubic inches and cubic feet. 6

26 6. a. Sample answer: Volume dish: V wh ( ) 96 in. 4 Estimate the amount eaten. It seems that the amount eaten has a length 6 inches, a width 6 inches, and a height inches. 4 Volume casserole eaten: V wh 66 ( ) 99in. 4 Volume mount left Total volume Volume eaten So, about 97 cubic inches casserole are left in the dish. b. Volume storage container: V wh in. ( )( ) The container holds 96 cubic inches and the amount left is about 97 cubic inches. So, the remaining casserole will not fit in the container. 7. face cube shaded face Number cubes in face Edge length face cube: A s 6 s 4 s 4 s Each cube is 4 centimeters long. So, the length the prism is 4 centimeters. The width is 4 centimeters. The height is 4 8 centimeters. V wh ( )( 8) 5 So, the volume is 5 cubic centimeters. 8. Answers should include, but is not limited to: a. Students should provide sketches tree house that has a surface area t most 400 square feet and a volume t least 50 cubic feet. They should explain their choice dimensions. b. For the dimensions to be reasonable, the tree house should be able to fit people and fit in a tree. Fair Game Review 9. x + 7 4; x 7? So, x 7 is a solution. 0.. x 6; x 5 5 5? So, x 5 is not a solution. x 9 4; x? So, x is not a solution.. C; The integers 4,,, 7, 0 are in the correct order. You can verify this by graphing each integer on a number line Quiz Use a net to find the area each face. Bottom: Side: 8 44 Side: 8 44 Side: 8 44 Side: ft 8 ft ft S So, the surface area is 40 square feet. 64

27 . Use a net to find the area each face Bottom: Side: 8 48 Side: 8 48 Side: 8 48 So, the surface area is 06.4 square meters. V wh , or 60 8 So, the volume is cubic yard. 8 V wh So, the volume is 8 cubic feet. V wh w 60 80w w ( w)( ) So, the width is 9 inches. S m m 0.4 m V wh ( )( ) So, the length is 7 inches. V wh 450 5( 0) h h h h So, the height is 7 inches. 8. Use a net to find the area each face. Bottom: Side: Side: Side: Side: cm 7.6 cm 4.8 cm So, the surface area the model is 0.7 square centimeters. S The layer is 7 cubes long and 7 cubes wide. So, you need 7 7, or 49 cubes to cover the the cube. To fill the cube, you need 7 layers 49 cubes. So, you need cubes to create a cube with an edge length 7 inches. 65

28 0. Volume toy chest : V Width toy chest : wh 5760 V 0( )( 6) wh ( w)( ) w w w The width toy chest is 5 inches. Chapter 8 Review. The solid has face on the, face on the, and 4 faces on the s. The faces intersect at different line segments. The edges intersect at 8 different points. So, the solid has 6 faces, edges, and 8 vertices. 6. Use a net to find the area each face. Top: Bottom: Front: Back: Side: Side: ft. The solid has face on the and 5 faces on the s. The faces intersect at 0 different line segments. The edges intersect at 6 different points. So, the solid has 6 faces, 0 edges, and 6 vertices Use a net to find the area each face. Top: 7 4 Bottom: 7 4 Front: Back: Side: 4 8 Side: in. in. in. in. 7 in. So, the surface area is 75 square feet. 7. Use a net to find the area each face. Top: Bottom: Front: Back: Side: Side: S m 9 m 9 m 9 m 6 m 4 m 4 in. S So, the surface area is 4 meters. S So, the surface area is 00 square inches. 66

29 8. Use a net to find the area each face. Front: Use a net to find the area each face. Top: 4 6 Back: Bottom: 4 6 Bottom: Front: Side: Side: Side: 8 4 Side: 4 8 m m 5 m 4 m 4 m 7 cm 8 m 5 cm 7 cm 8 cm 8 cm S cm So, the surface area is 400 square centimeters. S So, the surface area is 08 square meters. 0. Use a net to find the area each face. Bottom: Front: Back: Side: Side: ft 8 ft ft So, the surface area is 74 square feet. S

30 . Use a net to find the area each face. Bottom: 4 Side: Side: Side: in. in.. Use a net to find the area each face. Bottom: Side: Side: Side: Side: in. 7 cm 9.4 cm 7 cm So, the surface area is 6 square inches.. Use a net to find the area each face. Bottom: Side: Side: Side: So, the surface area is 47.6 square meters. S m 6.9 m 6 8 m 8 m S So, the surface area is 80.6 square centimeters. V wh , or 5 So, the volume is 5 cubic feet. V wh 5 6, or 6 8 So, the volume is 8 cubic feet. S Chapter 8 Test. The solid has face on the, face on the, and 6 faces on the s. The faces intersect at 8 different line segments. The edges intersect at different points. So, the solid has 8 faces, 8 edges, and vertices. 68

31 . The solid has face on the and 7 faces on the s. The faces intersect at 4 different line segments. The edges intersect at 8 different points. So, the solid has 8 faces, 4 edges, and 8 vertices.. Use a net to find the area each face. Top: 4 4 Bottom: 4 4 Front: Use a net to find the area each face. Bottom: Side: Side: Side: Back: 4 8 Side: Side: ft 4 ft ft 4 ft Side: in. in. in. ft So, the surface area is 8 square feet. S So, the surface area is 5 square inches. 6. Use a net to find the area each face. S Use a net to find the area each face. Bottom: 7 84 Front: 5 0 Back: 5 0 Side: 7 9 Side: ft ft ft 7 ft Bottom: Side: Side: Side: m 9.5 m m m So, the surface area is 70 square feet. S S So, the surface area is square meters. 69

32 V wh , or So, the volume is 4 cubic centimeters. 8 V wh 4 5, or 0 4 So, the volume is0 cubic centimeters. 0. The least amount wrapping paper needed to wrap the boxed DVD collection is equal to the surface area the boxed DVD collection. Use a net to find the area each face. Top: Bottom: Front: Back: Side: 8.5 Side: 8.5 S in. 8 in. 8 in. 8 in. 6 in. So, the least amount wrapping paper needed to wrap the boxed DVD collection is 8 square inches..5 in.. Use a net to find the area each face to be painted. Front: Back: Side: Side: To Be Painted 5. ft So, the surface area the part the ramp to be painted is square feet. Because you are going to paint the ramp with two coats, you will need enough paint to cover square feet. Because one quart paint covers 80 square feet and quarts, you should buy quarts paint to cover the ramp.. Volume original cube: V wh ( )( 4) Double the edge lengths: 4 8 Volume new cube: V wh 88 ()() 8 5 So, the volume the new cube is , or 8 times greater than the original cube. Chapter 8 Standards Assessment. B; You can translate the phrase never been above to mean less than or equal to. So, an inequality that represents the situation is t 8.. H; S ft 4 ft 6 ft 6 ft 70

33 . C; Volume the package: V 4. F; Number homes wh ( )( 6) So, the volume the package is 480 cubic inches. equals number homes built each year An equation is n 8y times number years plus number homes at start Variable: Let n be the number homes and y be the number years. n 8 y Part A: Part B: Use a net to find the area each face. Top: 6 7 Bottom: 6 7 Front: 8 96 Back: 8 96 Side: Side: in. in. 6 in. 6 in. 6 in. 6 in. 8 in. in. 8 in. 5..5, or ; 4m 6 4m m m.5 The solution is m, or C; Use a net to find the area each face. Bottom: 9 Side: So, the surface area the wooden box is 4 square inches. S Part C: yes; The -ounce sample wood stain can cover the box times, so you should have just enough to cover the box twice. Side: Side: Side: in. in. 5 in I; The length the green anole is 64 times greater than the length the crazy ant. 9. Castles 6 Towers S So, the surface area the figure is 9 square inches. The missing value is A; triangle rectangle A bh A w 46 ( ) ()() So, the area the figure is square units. 7

34

### VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.

Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:

### Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)

Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base

### Area of Parallelograms (pages 546 549)

A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular

### 6.3. Surface Area of Solids The Gift Box. My Notes ACTIVITY

Surface Area of Solids SUGGESTED LEARNING STRATEGIES: Activating Prior Knowledge J.T. is the creative director for a paper products company. The company is introducing a new line of gift boxes, called

### CC Investigation 4: Measurement

Content Standards 6.G., 6.G. CC Investigation : Measurement Mathematical Goals At a Glance PACING 3 days DOMAIN: Geometry Find the volume of a right rectangular prism with fractional edge lengths by packing

### *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review

### MD5-26 Stacking Blocks Pages 115 116

MD5-26 Stacking Blocks Pages 115 116 STANDARDS 5.MD.C.4 Goals Students will find the number of cubes in a rectangular stack and develop the formula length width height for the number of cubes in a stack.

### Geometry: Chapter Questions. 1. How is the formula for area of a parallelogram related to area of a rectangle?

Geometry: Chapter Questions. How is the formula for area of a parallelogram related to area of a rectangle?. How is the formula for area of a triangle related to area of a rectangle?. How do you find the

### 12-2 Surface Areas of Prisms and Cylinders. 1. Find the lateral area of the prism. SOLUTION: ANSWER: in 2

1. Find the lateral area of the prism. 3. The base of the prism is a right triangle with the legs 8 ft and 6 ft long. Use the Pythagorean Theorem to find the length of the hypotenuse of the base. 112.5

### Name: Date: Geometry Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry 2012-2013 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-7 HW: Pgs: 8-10 DAY 2: SWBAT: Calculate the Volume of

### 12-1 Representations of Three-Dimensional Figures

Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 12-1 Representations of Three-Dimensional Figures Use isometric dot paper to sketch each prism. 1. triangular

### Unit 8 Geometry. Introduction. Materials

Unit 8 Geometry Introduction In this unit, students will learn about volume and surface area. As they find the volumes of prisms and the surface areas of prisms and pyramids, students will add, subtract,

### 12 Surface Area and Volume

12 Surface Area and Volume 12.1 Three-Dimensional Figures 12.2 Surface Areas of Prisms and Cylinders 12.3 Surface Areas of Pyramids and Cones 12.4 Volumes of Prisms and Cylinders 12.5 Volumes of Pyramids

### Surface Area of Prisms

Surface Area of Prisms Jen Kershaw Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content,

### Grade 3 Math Expressions Vocabulary Words

Grade 3 Math Expressions Vocabulary Words Unit 1, Book 1 Place Value and Multi-Digit Addition and Subtraction OSPI words not used in this unit: add, addition, number, more than, subtract, subtraction,

### Area is a measure of how much space is occupied by a figure. 1cm 1cm

Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number

### Geometry Notes PERIMETER AND AREA

Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter

### Volume of Pyramids and Cones. Tape together as shown. Tape together as shown.

7-6 Volume of Pyramids and Cones MAIN IDEA Find the volumes of pyramids and cones. New Vocabulary cone Math Online glencoe.com Extra Examples Personal Tutor Self-Check Quiz In this Mini Lab, you will investigate

### 1. Kyle stacks 30 sheets of paper as shown to the right. Each sheet weighs about 5 g. How can you find the weight of the whole stack?

Prisms and Cylinders Answer Key Vocabulary: cylinder, height (of a cylinder or prism), prism, volume Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is

### Perimeter, Area, and Volume

Perimeter is a measurement of length. It is the distance around something. We use perimeter when building a fence around a yard or any place that needs to be enclosed. In that case, we would measure the

### Geometry and Measurement

The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

### 1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Replace 1 with 1 ft/12 in. 1ft

2 MODULE 6. GEOMETRY AND UNIT CONVERSION 6a Applications The most common units of length in the American system are inch, foot, yard, and mile. Converting from one unit of length to another is a requisite

### Area of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in

Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 Solve: Find the area of each triangle. 1. 2. 3. 5in4in 11in 12in 9in 21in 14in 19in 13in

### Algorithm set of steps used to solve a mathematical computation. Area The number of square units that covers a shape or figure

Fifth Grade CCSS Math Vocabulary Word List *Terms with an asterisk are meant for teacher knowledge only students need to learn the concept but not necessarily the term. Addend Any number being added Algorithm

### Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area. Determine the area of various shapes Circumference

1 P a g e Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area Lesson Topic I Can 1 Area, Perimeter, and Determine the area of various shapes Circumference Determine the perimeter of various

### Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to:

Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 Click the mouse button

### b = base h = height Area is the number of square units that make up the inside of the shape is a square with a side length of 1 of any unit

Area is the number of square units that make up the inside of the shape of 1 of any unit is a square with a side length Jan 29-7:58 AM b = base h = height Jan 29-8:31 AM 1 Example 6 in Jan 29-8:33 AM A

### Name: Date: Geometry Honors Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry Honors 2013-2014 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-6 HW: Pgs: 7-10 DAY 2: SWBAT: Calculate the Volume

### What You ll Learn. Why It s Important

These students are setting up a tent. How do the students know how to set up the tent? How is the shape of the tent created? How could students find the amount of material needed to make the tent? Why

### Geometry Notes VOLUME AND SURFACE AREA

Volume and Surface Area Page 1 of 19 VOLUME AND SURFACE AREA Objectives: After completing this section, you should be able to do the following: Calculate the volume of given geometric figures. Calculate

### Surface Area and Volume Nets to Prisms

Surface Area and Volume Nets to Prisms Michael Fauteux Rosamaria Zapata CK12 Editor Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version

### Integrated Algebra: Geometry

Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and

### 1) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-1) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = 7) (5)(-4) = 8) (-3)(-6) = 9) (-1)(2) =

Extra Practice for Lesson Add or subtract. ) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = Multiply. 7) (5)(-4) = 8) (-3)(-6) = 9) (-)(2) = Division is

### Covering and Surrounding: Homework Examples from ACE

Covering and Surrounding: Homework Examples from ACE Investigation 1: Extending and Building on Area and Perimeter, ACE #4, #6, #17 Investigation 2: Measuring Triangles, ACE #4, #9, #12 Investigation 3:

### Archdiocese of Washington Catholic Schools Academic Standards Mathematics

5 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions,

### 11-1. Space Figures and Cross Sections. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary

11-1 Space Figures and Cross Sections Vocabulary Review Complete each statement with the correct word from the list. edge edges vertex vertices 1. A(n) 9 is a segment that is formed by the intersections

### 12-6 Surface Area and Volumes of Spheres. Find the surface area of each sphere or hemisphere. Round to the nearest tenth. SOLUTION: ANSWER: 1017.

Find the surface area of each sphere or hemisphere. Round to the nearest tenth. 3. sphere: area of great circle = 36π yd 2 We know that the area of a great circle is r.. Find 1. Now find the surface area.

### 12-8 Congruent and Similar Solids

Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor. 3. Two similar cylinders have radii of 15 inches and 6 inches. What is the ratio

### Quick Reference ebook

This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

### TEKS TAKS 2010 STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM

7 th Grade Math TAKS-STAAR-STAAR-M Comparison Spacing has been deleted and graphics minimized to fit table. (1) Number, operation, and quantitative reasoning. The student represents and uses numbers in

### Precision and Measurement

NAME DATE PERIOD Precision and Measurement The precision or exactness of a measurement depends on the unit of measure. The precision unit is the smallest unit on a measuring tool. Significant digits include

### Activity Set 4. Trainer Guide

Geometry and Measurement of Solid Figures Activity Set 4 Trainer Guide Mid_SGe_04_TG Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development GEOMETRY AND MEASUREMENT OF SOLID FIGURES

### FCAT Math Vocabulary

FCAT Math Vocabulary The terms defined in this glossary pertain to the Sunshine State Standards in mathematics for grades 3 5 and the content assessed on FCAT in mathematics. acute angle an angle that

### II. Geometry and Measurement

II. Geometry and Measurement The Praxis II Middle School Content Examination emphasizes your ability to apply mathematical procedures and algorithms to solve a variety of problems that span multiple mathematics

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

### Surface Area and Volume

Surface Area and Volume 9 9. Surface Areas of Prisms 9. Surface Areas of Pyramids 9. Surface Areas of Cylinders 9.4 Volumes of Prisms 9.5 Volumes of Pyramids Pagodal roof that I want the I was thinking

### In Problems #1 - #4, find the surface area and volume of each prism.

Geometry Unit Seven: Surface Area & Volume, Practice In Problems #1 - #4, find the surface area and volume of each prism. 1. CUBE. RECTANGULAR PRISM 9 cm 5 mm 11 mm mm 9 cm 9 cm. TRIANGULAR PRISM 4. TRIANGULAR

### Unit 6 Measurement and Data: Area and Volume

Unit 6 Measurement and Data: Area and Volume Introduction In this unit, students will learn about area and volume. As they find the areas of rectangles and shapes made from rectangles, students will need

### Lesson 3.2 Perfect Squares, Perfect Cubes, and Their Roots Exercises (pages )

Lesson. Perfect Squares, Perfect Cubes, and Their Roots Exercises (pages 146 147) A 4. Use a calculator to write each number as a product of its prime factors, then arrange the factors in equal groups.

### Vocabulary Cards and Word Walls Revised: June 29, 2011

Vocabulary Cards and Word Walls Revised: June 29, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State Board of Education,

### 1. A plane passes through the apex (top point) of a cone and then through its base. What geometric figure will be formed from this intersection?

Student Name: Teacher: Date: District: Description: Miami-Dade County Public Schools Geometry Topic 7: 3-Dimensional Shapes 1. A plane passes through the apex (top point) of a cone and then through its

### 3D Geometry: Chapter Questions

3D Geometry: Chapter Questions 1. What are the similarities and differences between prisms and pyramids? 2. How are polyhedrons named? 3. How do you find the cross-section of 3-Dimensional figures? 4.

### Solving Geometric Applications

1.8 Solving Geometric Applications 1.8 OBJECTIVES 1. Find a perimeter 2. Solve applications that involve perimeter 3. Find the area of a rectangular figure 4. Apply area formulas 5. Apply volume formulas

### Author(s): Hope Phillips

Title: Fish Aquarium Math *a multi-day lesson Real-World Connection: Grade: 5 Author(s): Hope Phillips BIG Idea: Volume Designing and building aquariums includes mathematical concepts including, but not

### Height. Right Prism. Dates, assignments, and quizzes subject to change without advance notice.

Name: Period GL UNIT 11: SOLIDS I can define, identify and illustrate the following terms: Face Isometric View Net Edge Polyhedron Volume Vertex Cylinder Hemisphere Cone Cross section Height Pyramid Prism

### CONNECT: Volume, Surface Area

CONNECT: Volume, Surface Area 1. VOLUMES OF SOLIDS A solid is a three-dimensional (3D) object, that is, it has length, width and height. One of these dimensions is sometimes called thickness or depth.

### Lesson 11. Playing Board Games. 3 D Objects

Math 5 Lesson 11 3 D Objects Playing Board Games Zach has a new board game that he wants to play with his friends. He notices that the box the game is stored in is a lot like the prism he learned about

### RIT scores between 191 and 200

Measures of Academic Progress for Mathematics RIT scores between 191 and 200 Number Sense and Operations Whole Numbers Solve simple addition word problems Find and extend patterns Demonstrate the associative,

### Geo - CH10 Practice Test

Geo - H10 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. lassify the figure. Name the vertices, edges, and base. a. triangular pyramid vertices:,,,,

### ACTIVITY: Finding a Formula Experimentally. Work with a partner. Use a paper cup that is shaped like a cone.

8. Volumes of Cones How can you find the volume of a cone? You already know how the volume of a pyramid relates to the volume of a prism. In this activity, you will discover how the volume of a cone relates

### Area Long-Term Memory Review Review 1

Review 1 1. To find the perimeter of any shape you all sides of the shape.. To find the area of a square, you the length and width. 4. What best identifies the following shape. Find the area and perimeter

### Math Dictionary Terms for Grades K-1:

Math Dictionary Terms for Grades K-1: A Addend - one of the numbers being added in an addition problem Addition - combining quantities And - 1) combine, 2) shared attributes, 3) represents decimal point

### How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

### Practice: Space Figures and Cross Sections Geometry 11-1

Practice: Space Figures and Cross Sections Geometry 11-1 Name: Date: Period: Polyhedron * 3D figure whose surfaces are * each polygon is a. * an is a segment where two faces intersect. * a is a point where

### Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B

Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced

### Containers come in many different shapes such as cans, bottles and boxes. Which ones are prisms? Look at a selection of prisms and non-prisms.

SUPERMARKET BOXES Containers come in many different shapes such as cans, bottles and boxes. Which ones are prisms? Look at a selection of prisms and non-prisms. 1. What is necessary for a shape to be a

### Name: Class: Date: Geometry Chapter 3 Review

Name: Class: Date: ID: A Geometry Chapter 3 Review. 1. The area of a rectangular field is 6800 square meters. If the width of the field is 80 meters, what is the perimeter of the field? Draw a diagram

### 12-4 Volumes of Prisms and Cylinders. Find the volume of each prism.

Find the volume of each prism. 3. the oblique rectangular prism shown at the right 1. The volume V of a prism is V = Bh, where B is the area of a base and h is the height of the prism. If two solids have

### Area and Volume Equations

Area and Volume Equations MODULE 16? ESSENTIAL QUESTION How can you use area and volume equations to solve real-world problems? LESSON 16.1 Area of Quadrilaterals 6.8.B, 6.8.D LESSON 16. Area of Triangles

### Number Sense and Operations

Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents

### , where B is the area of the base and h is the height of the pyramid. The base

Find the volume of each pyramid. The volume of a pyramid is, where B is the area of the base and h is the height of the pyramid. The base of this pyramid is a right triangle with legs of 9 inches and 5

### ascending order decimal denominator descending order Numbers listed from largest to smallest equivalent fraction greater than or equal to SOL 7.

SOL 7.1 ascending order Numbers listed in order from smallest to largest decimal The numbers in the base 10 number system, having one or more places to the right of a decimal point denominator The bottom

### 11-1 Areas of Parallelograms and Triangles. Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary.

Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 2. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. Each pair of opposite

### 12-8 Congruent and Similar Solids

Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor. Ratio of radii: Ratio of heights: The ratios of the corresponding measures are

### Rectangular Prisms Dimensions

Rectangular Prisms Dimensions 5 Rectangular prisms are (3-D) three-dimensional figures, which means they have three dimensions: a length, a width, and a height. The length of this rectangular prism is

### 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B. Whole Numbers

Whole Numbers Scope and Sequence for Primary Mathematics, U.S. Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced or specifically addressed. Understand

### Geometry Chapter 12. Volume. Surface Area. Similar shapes ratio area & volume

Geometry Chapter 12 Volume Surface Area Similar shapes ratio area & volume Date Due Section Topics Assignment Written Exercises 12.1 Prisms Altitude Lateral Faces/Edges Right vs. Oblique Cylinders 12.3

### Geometry Unit 6 Areas and Perimeters

Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose

### 8-8 Volume and Surface Area of Composite Figures. Find the volume of the composite figure. Round to the nearest tenth if necessary.

Find the volume of the composite figure. Round to the nearest tenth if necessary. The figure is made up of a triangular prism and a rectangular prism. Volume of triangular prism The figure is made up of

### Algebra Geometry Glossary. 90 angle

lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:

### Kindergarten Math Standards at a Glance By the end of Kindergarten, students should be able to: Add and subtract numbers up to 5 Know number names

Kindergarten Math Standards at a Glance By the end of Kindergarten, students should be Add and subtract numbers up to 5 Know number names and count to 100 Count to tell the number of objects in a group

### Surface Area and Volume

1 Area Surface Area and Volume 8 th Grade 10 days by Jackie Gerwitz-Dunn and Linda Kelly 2 What do you want the students to understand at the end of this lesson? The students should be able to distinguish

### Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

### MATHEMATICS Grade 6 Standard: Number, Number Sense and Operations

Standard: Number, Number Sense and Operations Number and Number C. Develop meaning for percents including percents greater than 1. Describe what it means to find a specific percent of a number, Systems

### Surface Area and Volume

UNIT 7 Surface Area and Volume Managers of companies that produce food products must decide how to package their goods, which is not as simple as you might think. Many factors play into the decision of

### Kindergarten TEKS Vocabulary List

Kindergarten TEKS Vocabulary List Addition Equal parts First Half Less than More than Object Ordinal Quantity Same Second Sequence Set Subtraction Third Whole Count Patterns Predict Above Below Circles

### SURFACE AREA AND VOLUME

SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has

### Each pair of opposite sides of a parallelogram is congruent to each other.

Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. 2. Each pair of opposite

### CARMEL CLAY SCHOOLS MATHEMATICS CURRICULUM

GRADE 4 Standard 1 Number Sense Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers 1 and decimals relate to simple fractions. 4.1.1 Read and write

Task Model 1 DOK Level 1 6.G.A.1 Find the area of right triangles, other triangles, special polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques

### Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.

Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know

### 3Surface Area, Volume, and Capacity

124 Chapter 3Surface Area, Volume, and Capacity How much water do you think this water tank can hold? What would you need to know to calculate the exact amount? 3.1 Surface Area of Prisms REVIEW: WORKING

### Lesson 6. Identifying Prisms. Daksha and his brother and sister are playing a dice game. When a die is rolled, one number is displayed on the top.

Math 4 Lesson 6 Identifying Prisms Dice Games Daksha and his brother and sister are playing a dice game. When a die is rolled, one number is displayed on the top. When you roll the dice they will only

### 12-4 Volumes of Prisms and Cylinders. Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h

Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h The volume is 108 cm 3. The volume V of a prism is V = Bh, where B is the area of a base and h the

### G3-33 Building Pyramids

G3-33 Building Pyramids Goal: Students will build skeletons of pyramids and describe properties of pyramids. Prior Knowledge Required: Polygons: triangles, quadrilaterals, pentagons, hexagons Vocabulary:

### S.A. = L.A. + 2B = ph + 2B

Page 1 of 5 View Tutorial 5c Objective: Find the lateral area, total surface area, and volume of rectangular prisms. A prism is a polyhedron with two congruent & parallel bases. The other faces are the

### 3 rd 5 th Grade Math Core Curriculum Anna McDonald School

3 rd 5 th Grade Math Core Curriculum Anna McDonald School Our core math curriculum is only as strong and reliable as its implementation. Ensuring the goals of our curriculum are met in each classroom,

### Perfume Packaging. Ch 5 1. Chapter 5: Solids and Nets. Chapter 5: Solids and Nets 279. The Charles A. Dana Center. Geometry Assessments Through

Perfume Packaging Gina would like to package her newest fragrance, Persuasive, in an eyecatching yet cost-efficient box. The Persuasive perfume bottle is in the shape of a regular hexagonal prism 10 centimeters