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 5 6 0 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 4 5 0 unit cubes in each layer. Because there are 6 layers, there are 6 0 0 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 4 4 96 unit cubes in the prism. So, the volume is 96 cubic units. Section 8. 8. Activity (pp. 54 55). 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
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. 56 57). 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... 5. 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 7. 8. 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.. 4. 8. Exercises (pp. 58 59) Vocabulary and Concept Check. The statement is false. A triangular prism has two triangular faces. 5. 6.. The statement is true.. The statement is true. 4. The statement is false. A rectangular pyramid has four triangular faces. 40
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. 8. 5. 6. 9. 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.. 00. 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 ()() + 6 + 4 5 The area is 5 square feet.. A ( b b) h ( )( ). D; Because y and x, the statement y > x is true. 4
Section 8. 8. 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: 6 + 6 5 + 6 + 6 5 96 Base areas: 5 + 5 0 entire surface: 96 + 0 6 square units b. Base Net Lateral Face Net Lateral Face b. Lateral face areas: 6 + 5 6 + 4 6 7 Base areas: 4 + 4 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: 9 6 54 Bottom: 9 6 54 Front: 9 5 45 Back: 9 5 45 Side: 6 5 0 Side: 6 5 0 9 m Lateral Face Lateral Face Lateral Face 6 m 6 m 6 m 9 m Base 5 m 4. a. Lateral face areas: 5 4 + 4 6 + 5 4 64 Base areas: 6 4 + 6 4 4 entire surface: 88 square units S 54 + 54 + 45 + 45 + 0 + 0 58 So, the surface area is 58 square meters. Lateral face areas: + 5 + + 5 48 Base areas: 5 + 5 0 entire surface: 78 square units 4
. Use a net to find the area each face. Top: 5 5 5 Bottom: 5 5 5 Front: 5 6 Back: 5 6 Side: 5 6 Side: 5 6 5 in.. Use a net to find the area each face. Top: 8 0 80 Bottom: 8 0 80 Front: 8.5 8 Back: 8.5 8 Side: 0.5 5 Side: 0.5 5 0 ft 8 ft 0 ft 0 ft 8 ft. 5 in. 5 in. 5 in. 5 in. S 5 + 5 + 80 + + 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: 4 4 6 Front: 4 6 S 80 + 80 + 8 + 8 + 5 + 5 86 Back: 4 6 Side: 5 4 0 Side: 4 yd 4 yd 4 yd 5 yd 5 yd So, the surface area is 60 square yards. S 6 + 6 + 6 + 0 + 60 4
5. Use a net to find the area each face. Bottom: 6 9 44 Front: 6 6 48 Back: 6 6 48 Side: 0 9 90 Side: 0 9 90 0 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: 0. 8.6 88.58 Front: 8.6 6. 7.09 Back: 8.6 6. 7.09 Side: 0. 7.6 78.8 Side: 0. 7.6 78.8 0 m 9 m S 44 + 48 + 48 + 90 + 90 40 8. Exercises (pp. 64 65) 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 6 8 4 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: 6 7 4 Front: 6 8 4 Back: 6 8 4 Side: 0 7 70 Side: 8 7 56 0 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 4 + 4 + 4 + 70 + 56 6 So, the surface area is 99. square feet. S 88.58 + 7.09 + 7.09 + 78.8 + 78.8 99. 44
Practice and Problem Solving. 6. Use a net to find the area each face. Top: 0 5 50 Bottom: 0 5 50 Front: 0 0 Back: 0 0 Side: 5 5 Side: 5 5 0 ft Lateral face areas: 4 + 5 + 4 + 5 54 Base areas: 5 4 + 5 4 40 entire surface: 54 + 40 94 square units 0 ft ft 4. S 50 + 50 + 0 + 0 + 5 + 5 0 So, the surface area is 0 square feet. 5. Lateral face areas: 5 + 5 5 + 4 5 60 Base areas: 4 + 4 entire surface: 60 + 7 square units 7. Use a net to find the area each face. Top: 6 9 54 Bottom: 6 9 54 Front: 6 8 Back: 6 8 Side: 9 7 Side: 9 7 6 cm 9 cm 9 cm 9 cm 6 cm cm Lateral face areas: 6 7 + 7 + 6 7 + 7 6 Base areas: 6 + 6 6 entire surface:6 + 6 6 square units S 54 + 54 + 8 + 8 + 7 + 7 98 So, the surface area is 98 square centimeters. 45
8. Use a net to find the area each face. Top: 4 8 Bottom: 4 8 Front: 5 0 Back: 5 0 Side: 4 5 0 Side: 4 5 0 yd 0. Use a net to find the area each face. Bottom: 0 6 60 Front: 6 5 0 Back: 6 5 0 Side: 0 7 70 Side: 0 7 70 4 yd 7 m 5 m 7 m 4 yd 4 yd yd 7 m 6 m 7 m 0 m 5 yd S 8 + 8 + 0 + 0 + 0 + 0 76 S 60 + 0 + 0 + 70 + 70 740 So, the surface area is 740 square meters.. Use a net to find the area each face. Top: 4 4 8 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: 4 4 8 Back: 5.7 7. Side: 4 Side: 4 4 mm 4 mm 5.7 mm 4 mm mm ft S 8 + 8 + 7. + + 57. So, the surface area is 57. square millimeters. S 6.6 + + + 6 + 7.6 So, the surface area is 7.6 square feet. 46
. 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: 8 8 64 Bottom: 8 8 64 Front: 8 0 80 Back: 8 0 80 Side: 8 0 80 Side: 8 0 80 8 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: 6 7 4 Side: 5 7 5 Side: 5 7 5 6 ft 4 ft 0 in. 7 ft S 64 + 64 + 80 + 80 + 80 + 80 448 So, the least amount wrapping paper needed to wrap the gift box is 448 square inches. S + + 4 + 5 + 5 6 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: 6.5 5 Front: 6 4 4 Back: 6 4 4 Side:.5 4 0 Side:.5 4 0 4 ft... 6 ft 6 ft S 5 + 4 + 4 + 0 + 0 8 So, the surface area is 8 square feet, which is the amount glass used. 47
5. area Box : Use a net to find the area each face. Top: 0 6 0 Bottom: 0 6 0 Front: 0 4 80 Back: 0 4 80 Side: 6 4 4 Side: 6 4 4 0 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 $94.44 9 ft area Box : Use a net to find the area each face. Top: 5 4 60 Bottom: 5 4 60 Front: 5 8 0 Back: 5 8 0 Side: 4 8 Side: 4 8 4 in. S 0 + 0 + 80 + 80 + 4 + 4 448 5 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 $84.0 8 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: 5 6 4 Back: 5 6 4 5 Side: 5 5 5 5 Side: 5 0 To Be Painted S 6 4 + 87 6 4 + 5 5 + 5 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 87 00.88 quarts, you should buy quarts stain to cover the ramp. S 60 + 60 + 0 + 0 + + 44 48
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: 9 8 7 Bottom: 9 8 7 Front: 9 5 45 Back: 9 5 45 Side: 8 5 40 Side: 8 5 40 9 ft 8 ft area rectangular prism before removing cube cube cube cube cube cube cube 8 ft 8 ft 9 ft S 4 5 5 + 5 + 5 + 5 + 5 64 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: 5 5 5 Bottom: 5 5 5 Front: 5 5 5 Back: 5 5 5 Side: 5 5 5 Side: 5 5 5 S 7 + 7 + 45 + 45 + 40 + 40 4 Fair Game Review 8. A bh ()(8) 48 9. 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 4 4 4 0? So, x 4 is not a solution. 49
Study Help Available at BigIdeasMath.com. Quiz 8. 8.. 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: 5 0 50 Side: 0 0 Side: 4 0 40 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 6 + 6 + 50 + 0 + 40 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 8 + 8 + + + 6 + 6 5 So, the surface area is 5 square inches. 50
9. a. Use a net to find the area each face. Top: 9 4 6 Bottom: 9 4 6 Front: 9 08 Back: 9 08 Side: 4 48 Side: 4 48 9 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 6 + 6 + 08 + 08 + 48 + 48 84 So, the surface area the cereal box is 84 square inches. S 4 + 4 + 88 + 88 + + 90 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 84 90 94 square inches. 5
0. Use a net to find the area each face. Bottom: 0 5 00. Front: 5 6 5 Back: 5 6 5 Side: 0 6.5 0 Side: 0 6.5 0 0 cm lateral face lateral face base lateral face 6.5 cm 6.5 cm 5 cm S 00 + 5 + 5 + 0 + 0 90 6.5 cm 6 cm Sample answer: lateral faces: 6 6 + 6 6 + 6 6 54 Base area: 6 5 5 entire surface: 54 + 5 69 The surface area the triangular pyramid is 69 square units. 4. a. So, the surface area the gift box is 90 square centimeters. Section 8. 8. Activity (pp. 68 69). 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: 6 8 + 6 8 + 6 8 + 6 8 96 Base area: 6 6 6 entire surface: 96 + 6 So, the area the square pyramid is square units. lateral faces: 4 + 4 + 4 + 4 4 Base area: 9 entire surface: 4 + 9 The surface area the square pyramid is square units. b. 5 lateral faces: 5 5 + 5 5 + 5 5 + 5 5 50 Base area: 5 5 5 entire surface: 50 + 5 75 The surface area the square pyramid is 75 square units.
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: 5 5 5 Side: 5 5.5 Side: 5 5.5 Side: 5 5.5 Side: 5 5.5 5 cm 5 cm 5 cm Side: Side: ft ft ft S 5 +.5 +.5 +.5 +.5 75 So, the surface area is 75 square centimeters. So, the surface area is 6 square feet. S 4 + + + + 6. Use a net to find the area each face. Bottom: 4 4 6 Side: 4.6 7. Side: 4.6 7. Side: 4.6 7. Side: 4.6 7. 4 in..6 in. 4 in. So, the surface area is 44.8 square inches. S 6 + 7. + 7. + 7. + 7. 44.8 5
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: 0 7. 7 Side: 0 0 Side: 0 0 Side: 0 0 0 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: 9 7.8 5. Side: 7 9.5 Side: 7 9.5 S.7 + + + 0.7 So, the surface area is 5 square yards. 8. Exercises (pp. 7 7) S 7 + 0 + 0 + 0 5 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: 7 9.5 9 in. 7.8 in. 7 in. S 5. +.5 +.5 +.5 9.6 So, the surface area is 9.6 square inches. 54
Practice and Problem Solving. 5. lateral faces: + + + 8 base: 9 entire surface: 8 + 9 7 The surface area the figure is 7 square units. 4. lateral faces: 8 6 + 8 6 + 8 6 + 8 6 96 base: 8 8 64 entire surface: 96 + 64 60 The surface area the figure is 60 square units. 6. Use a net to find the area each face. Bottom: 7 7 49 Side: 7 5 7.5 Side: 7 5 7.5 Side: 7 5 7.5 Side: 7 5 7.5 7 in. 5 in. lateral faces: 5 4 + 5 4 + 5 4 + 5 4 40 base: 5 5 5 entire surface: 40 + 5 65 The surface area the figure is 65 square units. S 49 + 7.5 + 7.5 + 7.5 + 7.5 9 So, the surface area is 9 square inches. 55
7. Use a net to find the area each face. Bottom: 6 6 6 Side: 6.4 4. Side: 6.4 4. Side: 6.4 4. 8. Use a net to find the area each face. Bottom: 44 Side: 7 0 Side: 7 0 Side: 7 0 Side: 6.4 4. Side: 7 0 cm 7 cm 6 yd.4 yd S 44 + 0 + 0 + 0 + 0 55 So, the surface area is 7.8 square yards. S 6 + 4. + 4. + 4. + 4. 7.8 So, the surface area is 55 square centimeters. 9. Use a net to find the area each face. Bottom: 0.4 6.4 Side: 9 54 Side: 9 54 Side: 9 54 9 ft ft 0.4 ft S 6.4 + 54 + 54 + 54 4.4 So, the surface area is 4.4 square feet. 56
0. Use a net to find the area each face. Bottom: 8 6.9 7.6 Side: 4 8 56 Side: 4 8 56 Side: 4 8 56. Use a net to find the area each face. Bottom: 4.5 7 Side: 4 8 6 Side: 4 8 6 Side: 4 8 6 8 in. 6.9 in. 8 m 4 m.5 m 4 in. S 7.6 + 56 + 56 + 56 95.6 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 7 + 6 + 6 + 6 55 Side:.. Side:.. Side:... in. in..7 in. S.7 + + + 7.7 So, the surface area the paperweight is 7.7 square inches. 57
. Use a net to find the area each triangular face. 5. Use a net to find the area each face. Bottom: 6 6 6 6 ft 6 ft 9.7 ft Side: 6 9.7 58.6 Side: 6 9.7 58.6 Side: 6 x x Side: 6 x x Side: 6 x x Side: 6 x x 6 in. x Side: 6 9.7 58.6 6 in. Side: 6 9.7 58.6 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 58.6 + 58.6 + 58.6 + 58.6,74.4 ft ft ft The value x is 4 inches. 84 6 + x + x + x + x 84 6 + x 48 x 4 x S + + + 8 So, the surface area the light cover is 8 square feet. The weight the cover is 8.45 9.6 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
6. The area the base is 6 times the area triangle with a base 8 centimeters and a height 6.9 centimeters. base: 6 8 6.9 66. cm Use a net to find the area each face the pyramid. Bottom: 6 8 6.9 66. 7. 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 7 4 8 Turtles 6 The equivalent ratios are: 7 to, 4 to 6, and 8 to. Side: 8 5 9. Apples 0 5 0 Oranges 4 The equivalent ratios are: 0 to 4, 5 to, and 0 to. 66. cm 8 cm cm 0. B; Quadrant II ( 7, ) 8 7 6 5 4 O (, ) Quadrant III 8 7 6 5 4 4 5 6 7 8 y Quadrant I (, 4) 4 5 6 7 8 x (5, ) Quadrant IV S 66. + 5 + 5 + 5 + 5 + 5 + 5 478. The point (, ) is in the third quadrant. So, the surface area the hexagonal pyramid is 478. square centimeters. 59
Section 8.4 8.4 Activity (pp. 74 75). 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 4 4 4 m m So, the volume the rectangular prism is cubic meter. 6 6 60
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 4 4 4 5 48 4, 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. 60 5. 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. 76 77). 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. 60 60 5 4 5 in.. V wh 4 4 4 7 64 So, the volume is 7 64 cubic yard.. V wh 0() 8 4 760 4 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
4. 5. V wh 7 6 7 7 6 ( )( ) The length is 6 inches. V wh 75 0( w) 5 75 0w 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: 5 7 5 Bottom: 5 7 5 Front: 5 0 50 Back: 5 0 50 Side: 7 0 70 Side: 7 0 70 5 cm 7 cm 7 cm 7 cm 5 cm 8.4 Exercises (pp. 78 79) 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 5 + 5 + 50 + 50 + 70 + 70 0 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 5 4 0 So, the volume is 0 cubic inch. 6
5. 6. 7. 8. 9. 0. V wh 7 4 5, or 6 6 So, the volume is 5, or 6 6 V wh 5 5 5 8 5 So, the volume is 8 5 V wh 5 8 4 5 6 ( ) So, the volume is 5 6 V wh 5 6 4 8 cubic foot. cubic meter. cubic centimeters. So, the volume is 8 cubic centimeters. V wh 4 5 7 8 So, the volume is cubic meters. V wh ( ) 60 9 9 h 60 8h 60 8h 8 8 0 h So, the height is 0 centimeters... V wh ( w)( ) 0.5 7 7 0.5 49w 0.5 49w 49 49 4.5 w So, the width is 4.5 centimeters. V wh 5 9( w) 4 5.5w 5.5w.5.5 6 w So, the width is 6 inches.. V wh ()( ).5.5.75 The volume the water in the tank when it is full is.75 cubic feet. The weight the water is.75 6.4 4 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 6 56 4096 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 44 78 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
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 96 99 97 So, about 97 cubic inches casserole are left in the dish. b. Volume storage container: V wh 7 7 4 96 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 96 6 6 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? 7 + 7 4 4 4 So, x 7 is a solution. 0.. x 6; x 5 5 5? 6 5 7 6 So, x 5 is not a solution. x 9 4; x? 9 4 4 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. 4 0 4 5 6 7 8 9 0 Quiz 8. 8.4. Use a net to find the area each face. Bottom: 8 8 64 Side: 8 44 Side: 8 44 Side: 8 44 Side: 8 44 8 ft 8 ft ft S 64 + 44 + 44 + 44 + 44 40 So, the surface area is 40 square feet. 64
. Use a net to find the area each face.. 4. 5. Bottom: 0.4 6.4 Side: 8 48 Side: 8 48 Side: 8 48 So, the surface area is 06.4 square meters. V wh 4 5 5 8 4 60, or 60 8 So, the volume is cubic yard. 8 V wh 4 5 8 So, the volume is 8 cubic feet. V wh 60 5 60 80w 60 80w 80 80 9 w ( w)( ) So, the width is 9 inches. S 6.4 + 48 + 48 + 48 06.4 8 m m 0.4 m 6. 7. V wh ( )( ) 54 54 54 7 So, the length is 7 inches. V wh 450 5( 0) h 450 50h 450 50h 50 50 7 h So, the height is 7 inches. 8. Use a net to find the area each face. Bottom: 7.6 7.6 57.76 Side: 7.6 4.8 8.4 Side: 7.6 4.8 8.4 Side: 7.6 4.8 8.4 Side: 7.6 4.8 8.4 7.6 cm 7.6 cm 4.8 cm So, the surface area the model is 0.7 square centimeters. S 57.76 + 8.4 + 8.4 + 8.4 + 8.4 0.7 9. 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 7 49 4 cubes to create a cube with an edge length 7 inches. 65
0. Volume toy chest : V Width toy chest : wh 5760 V 0( )( 6) wh ( w)( ) 5760 4 6 5760 84w 5760 84w 84 84 5 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: 7.5 5 7.5 Bottom: 7.5 5 7.5 Front: 7.5 4 0 Back: 7.5 4 0 Side: 5 4 0 Side: 5 4 0 7. 7. 4 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.. 4. 5. Use a net to find the area each face. Top: 7 4 Bottom: 7 4 Front: 7 4 8 Back: 7 4 8 Side: 4 8 Side: 4 8 7 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: 6 9 54 Bottom: 6 9 54 Front: 6 4 7 Back: 6 4 7 Side: 9 4 40.5 Side: 9 4 40.5 S 7.5 + 7.5 + 0 + 0 + 0 + 0 75 6 m 9 m 9 m 9 m 6 m 4 m 4 in. S 4 + 4 + 8 + 8 + 8 + 8 00 So, the surface area is 4 meters. S 54 + 54 + 7 + 7 + 40.5 + 40.5 4 So, the surface area is 00 square inches. 66
8. Use a net to find the area each face. Front: 8 5 60 9. Use a net to find the area each face. Top: 4 6 Back: 8 5 60 Bottom: 4 6 Bottom: 7 8 56 Front: 5 8 40 Side: 7 7 9 Side: 7 5 05 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 6 + 6 + 40 + 4 + 08 7 cm So, the surface area is 400 square centimeters. S 56 + 60 + 60 + 9 + 05 400 So, the surface area is 08 square meters. 0. Use a net to find the area each face. Bottom: 8 5 40 Front: 6 5 5 Back: 6 5 5 Side: 8 6.5 5 Side: 8 6.5 5 6 ft 8 ft 6. 6. 6 ft So, the surface area is 74 square feet. S 40 + 5 + 5 + 5 + 5 74 67
. 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: 7 7 49 Side: 7 9.4.9 Side: 7 9.4.9 Side: 7 9.4.9 Side: 7 9.4.9 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: 8 6.9 7.6 Side: 8 0 40 Side: 8 0 40 Side: 8 0 40 So, the surface area is 47.6 square meters. S 4 + + + + 0 m 6.9 m 6 8 m 8 m S 7.6 + 40 + 40 + 40 47.6 4. 5. So, the surface area is 80.6 square centimeters. V wh 5 4 60, or 5 So, the volume is 5 cubic feet. V wh 5 6, or 6 8 So, the volume is 8 cubic feet. S 49 +.9 +.9 +.9 +.9 80.6 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
. 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: 4 8 5. 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 4 + 4 + 8 + 8 + + 8 So, the surface area is 5 square inches. 6. Use a net to find the area each face. S + + + + 5 4. Use a net to find the area each face. Bottom: 7 84 Front: 5 0 Back: 5 0 Side: 7 9 Side: 5 7 5 ft ft ft 7 ft Bottom: 9.5 5.5 Side: 5 8.5 Side: 5 8.5 Side: 5 8.5 5 m 9.5 m m m So, the surface area is 70 square feet. S 84 + 0 + 0 + 9 + 5 70 S 5.5 + 8.5 + 8.5 + 8.5 99.75 So, the surface area is 99.75 square meters. 69
7. 8. 9. V wh 5 7 4 05, or 4 4 8 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: 6 8 48 Bottom: 6 8 48 Front: 6.5 9 Back: 6.5 9 Side: 8.5 Side: 8.5 S 48 + 48 + 9 + 9 + + 8 6 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: 4 6 4 Back: 4 6 4 Side: 5. 9.5 96.4 Side: 6 9.5 7 9. To Be Painted 5. ft So, the surface area the part the ramp to be painted is 497.4 square feet. Because you are going to paint the ramp with two coats, you will need enough paint to cover 497.4 994.8 square feet. Because one quart paint covers 80 square feet and 994.8 80.45 quarts, you should buy quarts paint to cover the ramp.. Volume original cube: V wh 64 44 ( )( 4) Double the edge lengths: 4 8 Volume new cube: V wh 88 ()() 8 5 So, the volume the new cube is 5 64 8, 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; 4 + 6 6 + 6 48 + 6 48 + 5 S 4 + 4 + 96.4 + 7 497.4 5. ft 4 ft 6 ft 6 ft 70
. C; Volume the package: V 4. F; Number homes wh 480 80 ( )( 6) So, the volume the package is 480 cubic inches. equals number homes built each year An equation is n 8y + 60. times number years plus number homes at start Variable: Let n be the number homes and y be the number years. n 8 y + 60 7. 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: 6 8 48 Side: 6 8 48 in. in. 6 in. 6 in. 6 in. 6 in. 8 in. in. 8 in. 5..5, or ; 4m 6 4m 6 4 4 m m.5 The solution is m, or.5. 6. C; Use a net to find the area each face. Bottom: 9 Side: 5 7.5 So, the surface area the wooden box is 4 square inches. S 7 + 7 + 96 + 96 + 48 + 48 4 Part C: yes; The -ounce sample wood stain can cover the box 900 4. times, so you should have just enough to cover the box twice. Side: 5 7.5 Side: 5 7.5 Side: 5 7.5 in. in. 5 in. 6 8. I; 6 6 64 The length the green anole is 64 times greater than the length the crazy ant. 9. Castles 6 Towers 4 8 4 48 S 9 + 7.5 + 7.5 + 7.5 + 7.5 9 So, the surface area the figure is 9 square inches. The missing value is 6. 0. A; triangle rectangle A bh A w 46 ( ) ()() 8 4 8 So, the area the figure is 8 + 4 square units. 7