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 Slant height Lateral Face Surface area Lateral Edge Lateral surface area Orthographic View Right Prism Oblique Prism Altitude Base Sphere Great Circle Friday, 3/8 Dates, assignments, and quizzes subject to change without advance notice. Monday Tuesday Block Day Friday 8 Basics SPRING BREAK 18 Prisms and Pyramids 25 Dimensional Changes Views and Faces: Chapter 10 sections 1-3 19 Cylinders, Cones, and Spheres 26 Review 20/21 Applications 27/28 I can identify and draw orthographic and isometric views I can identify the number of faces, edges, and vertices I can identify the cross-sections of solid figures I can match solids and nets I can identify and draw orthographic and isometric views PRACTICE: Solids View and Net Practice Worksheet TEST 22 Composites Monday, 3/18 Prisms and Pyramids: Chapter 10 sections 4-7 I can classify prisms and pyramids I can find the surface areas and volume of solids I can solve problems using surface areas and volume PRACTICE: Prism and Pyramids Worksheet Tuesday, 3/19 Cylinders, Cones, and Spheres: Chapter 10 sections 4-8 I can find the surface areas and volume of solids I can solve problems using surface areas and volume PRACTICE: Cylinders, Cones, and Spheres Worksheet Block, 3/20-21 Applications I can find the surface areas and volume of solids I can solve problems using surface areas and volume PRACTICE: Applications Worksheet 1
Friday, 3/22 Composites I can find the surface areas and volume of composite solids I can solve problems using surface areas and volume PRACTICE: Composite Worksheet Monday, 3/25 Dimensional Changes I can determine the effect on surface areas and volume when one or more dimensions are changed PRACTICE: Dimensional Changes Worksheet Tuesday, 3/26 Review I can assess my strengths and weaknesses on all previously learned material. PRACTICE: Review Activity Block day, 3/27-28 Test Unit #11: Solids I can demonstrate my ability on all previously learned material. 2
Notes: Surface Area and Volume of Prisms and Pyramids I. Vocabulary There are two of a solid. The surface area is the amount of surface on the of the solid. This does NOT include the. The surface area is the amount of surface on faces. The of a solid is how much they can hold. It is measured in measurements. II. Prisms Formulas: Lateral Surface area = Total Surface Area = Volume = The P stands for the of the. The B stands for the of the and the h stands for the. In other words you have to for the P and the B and the h is a. Examples: 3 in 8.7 ft 4 in 15 in 10 ft 31 ft LSA = SA = V = LSA = SA = V = 3 LSA = SA = 5 2 V = 3
III. Pyramids Formulas: Lateral Surface area = Total Surface Area = Volume = The, h, of a regular Pyramid is the distance from the to the of the base. The, l, of a regular pyramid is the of a lateral face. Examples: 24 cm 26 cm 20 cm LSA = SA = V = 20 cm LSA = SA = V = 15 m (l) (l) 12 m (h) LSA = SA = V = 9 m (a) 18 3 m 4
Assignment Prisms and Pyramids For each solid, find the lateral surface area (LSA), total surface area (SA), and volume (V). 1. LSA = 2. LSA = 16 cm 5 cm 8 cm 3. LSA = 4. LSA = 5. LSA = 12cm 13 cm 6. LSA = 10 cm 10 cm 6 m 8 m 2 m 25 m (l) (l) 7. LSA = 8. LSA = 24 m (h) 7 m (a) 14 3 m 5
9. The base of a triangular prism is an equilateral triangle with a perimeter of 24 inches. If the height of the prism is 5 inches, find the lateral area. F) 120 in 2 G) 60 in 2 H) 40 in 2 J) 360 in 2 10) Find the surface area, lateral surface area and volume of a rectangular prism with height 7 m, length 10 m, and width 8 m. 11) What equation would be used to find the surface area for the pyramid? A) C) 1 1 S = (36)(4) + 2(36) B) S = (36)(5) + 2(36) 2 2 1 1 S = (24)(5) + 36 D) S = (24)(4) + 36 2 2 12) What equation would be used to find the lateral surface area of a right triangular prism? (10)(24) 10 + 24 A) S = (10 + 24 + 26)(7) + 2( ) B) S = (10 + 24 + 7)(26) + ( ) 2 2 C) S = (24 + 24 + 7 + 7)(10) + 2(24)(7) D) S = (10 + 24 + 26)(7) + 2(10)(24) 26 m 10 m 7 m 24 m 13) What equation would be used to find the volume for the pyramid with apothem of 5.5 cm, a side length of 8 cm, and a height of 10 cm? 1 1 1 (5.5)(40) A) V = ( )(5.5)(8)(10) B) V = (10) 3 2 3 2 1 (5.5)(8) 1 C) V = (10) D) V = (5.5)(8)(10) 3 2 3 14) What is the area of this triangle, to the nearest square inch? A) 22 in 2 B) 38 in 2 C) 43 in 2 D) 75 in 2 15) The hypotenuse of a right triangle is 89 units. One leg is 39 units. What is the length of the other leg? A) 50 units B) 62 units C) 80 units D) 97 units 6
Cylinders Cylinders - Notes Prisms Cylinder Formulas: L,, V = 15 m LSA = What is height of cylinder? What is radius of cylinder? 43 m What does B stand for? YOU TRY: LSA = 8 cm 12 cm Spheres - Notes Sphere Formulas: Surface Area =, Volume = YOU TRY: 7
Cylinders Cones - Notes Cones Cone Formulas: L,, What is the height of the cone? What is the radius of the base? What is the slant height of the cone? LSA = YOU TRY: 4 m LSA = 16 m 8
Cylinders, Cones, and Spheres Worksheet 1. LSA = 2. LSA = 3. LSA = 4. LSA = 5. LSA = 6. 7. 8. 9. Find the diameter of a cone with slant height 18 and lateral surface area 162π. 10. Susan has a fish tank in the shape of a cylinder that is 26 inches tall. The diameter of the tank is 12 inches. If there are 2 inches of rocks in the bottom, how much water is needed to fill the tank? 11. 9
12. For small paving jobs, a contractor uses a roller pushed by a worker. What is the area of pavement with which the surface of the roller will come into contact in one complete rotation? 13. 14. 15. 10
Notes Applications of Solid Figures 1. Find the height of a cylinder with a surface area of 160π ft 2 and radius of 5 ft. 2. Abigail has a cylindrical candle mold with the dimensions shown. If Abigail has a rectangular block of wax measuring 15 cm by 12 cm by 18 cm, about how many candles can she make after melting the block of wax? A) 14 B) 31 C) 35 D) 76 3. Michael is refinishing the bookcase pictured to the left. How much area will he cover if he only paints the left side, right side, and back of the book case with two coats? 4 ft 6 ft 6 in. 4. The Imaginary Toy Company, has increased their size of the Creativity Doll. The packaging department has calculated that they need to add 3 inches to each of the dimension of the original packaging (Original is shown in Picture). What is the new amount of cardboard needed to package one doll? 10 in 5. 5 in 3 in 11
Practice and Applications 1. The greater the lateral area of a florescent light bulb, the more light the bulb produces. One cylindrical light bulb is 16 inches long with a 1 inch radius. Another is 23 inches long with a ¾ inch radius. Which bulb produces more light? 2. The base of a triangular prism is an equilateral triangle with a perimeter of 24 inches. If the height of the prism is 5 inches, find the lateral area. F) 120 in 2 G) 60 in 2 H) 40 in 2 J) 360 in 2 3. A juice container is a square prism with base edge length 4 in. When an 8 in. straw is inserted into the container as shown, exactly 1 in. remains outside the container. a) How much of the straw is in the container? b) Find BC c) Use BC and the straw to find AC d) Now use the height (answer to part c) to find how much material is required to manufacture the container. Round to the nearest tenth. 4. 5. Which of the following equations would answer the problem below? Susan has a fish tank in the shape of a cylinder that is 26 inches tall. The diameter of the tank is 12 inches. If there are 2 inches of rocks in the bottom, how much water is needed to fill the tank? A) 2 V = π (12) (26) B) 2 V = π (6) (26) C) 2 V = π (12) (24) D) 2 V = π (6) (24) 12
6. 7. If one gallon of paint covers 250 square feet, how many gallons of paint will be needed to cover the shed, not including the roof? If a gallon of paint costs $25, about how much will it cost to paint the walls of the shed? 8. Colin is buying dirt to fill a garden bed that is a 9 ft by 16 ft rectangle. If he wants to fill it to a depth of 4 in., how many cubic yards of dirt does he need? If dirt costs $25 per yd 3, how much will the project cost? (Hint: 1 yd 3 = 27 ft 3 ) 9. The base of a triangular prism is an equilateral triangle with a perimeter of 24 inches. If the height of the prism is 5 inches, find the lateral area. F) 120 in 2 G) 60 in 2 H) 40 in 2 J) 360 in 2 7. 8. 13
10. A right circular cylinder has a volume of 1,000 cubic inches and a height of 8 inches. What is the radius of the cylinder to the nearest tenth of an inch? A) 6.3 in B) 11.2 in C) 19.8 in D) 39.8 in 11. 12. 13. 14. 15. 16. 14
17. 18. 19. 20. 15
Prisms and Pyramid: Composite and Nets Notes and Assignment A composite figure is made up of or more geometric figures combined. **Keep in mind that some of the sides may not be in the surface area if they are now part of the interior of the figure. Polyhedron a figure with surfaces Example 1 Example 2 LSA = Faces - Edges - Vertices - Example 3 & 4: 4 in LSA = LSA = 8 in 10 in 5. 6. _ 16
7. If one gallon of paint covers 250 square feet, how many gallons of paint will be needed to cover the shed, not including the roof? If a gallon of paint costs $25, about how much will it cost to paint the walls of the shed? 8. Find the height of a rectangular prism with length 5 ft, width 9 ft, and volume 495 ft 3. 9. Colin is buying dirt to fill a garden bed that is a 9 ft by 16 ft rectangle. If he wants to fill it to a depth of 4 in., how many cubic yards of dirt does he need? If dirt costs $25 per yd 3, how much will the project cost? (Hint: 1 yd 3 = 27 ft 3 ) 10. You can use displacement to find the volume of an irregular object, such as a stone. Suppose the tank shown is filled with water to a depth of 8 in. A stone is placed in the tank so that it is completely covered, causing the water level to rise by 2 in. Find the volume of the stone. 11. 12. 17
13. Which of the following equations can NOT be used to find the volume? A) V = π (2 2 )(4) + (12)(4)(4) B) V = 16π + (192) C) V = ½ [π (2 2 )(4)] + (12)(4)(4) D) V = 4π (4) + (12)(4)(4) The answer is. The others don t work because.. 14. Abigail has a cylindrical candle mold with the dimensions shown. If Abigail has a rectangular block of wax measuring 15 cm by 12 cm by 18 cm, about how many candles can she make after melting the block of wax? A) 14 B) 31 C) 35 D) 76 15. The answer is. The others don t work because.. 18
16. The answer is. The others don t work because.. 17. The answer is. The others don t work because.. 18. Describe the steps needed to solve this problem:. 19
Dimensional Changes in Volume Review: What will happen to the PERIMETER of a similar figure when you multiply the dimensions by any scale factor? What happens to the AREA of a similar figure when you change the dimensions by a scale factor? Extend to Volume: A. Find the volume of a 1 x 2 x 3 rectangular prism. The volume is. Now find the volume for a similar rectangular prism whose dimensions are double the dimensions of the first prism. The new volume is. When you double the dimensions of a rectangular prism, the volume is times the volume of the original prism. B. Find the volume of a cube with an edge of 4 units. The volume is. Now find the volume for a similar cube whose dimensions are half the dimensions of the first prism. The new volume is. When you half the dimensions of a figure, the volume is times the volume of the original figure. A B Original Scale factor Volume Scale factor Conclusion: What happens to the VOLUME of a similar solid when you change the dimensions by a scale factor? 20
Examples: 1. 2. 2006 Exit Modified 3. Campbell s manufactures a cylindrical soup can that has a diameter of 6 inches and a volume of 226 in 3. If the stays height the same and the diameter is doubled, what will happen to the can s volume? A B C D It will remain the same. It will double. It will triple. It will quadruple. 4. If the volume of a cube is increased by a factor of 8, what is the change in the length of the sides of the cube? 5. Describe the change to the surface area and volume of the cylinders. Why is the following not a dimensional change problem? 6. The radius of a spherical beach ball is 24 centimeters. If another spherical beach ball has a radius 3 centimeters longer, about how much greater is its volume, to the nearest cubic centimeter? 21
Dimensional Changes Worksheet 1. If the volume of a cube is increased by a factor of 1, what is the change in the length of the sides of 8 the cube? 2. A rectangular solid has a volume of 24 cubic decimeters. If the length, width, and height are all changed to 1 their original size, what will be the new volume of the rectangular solid? 2 A 3 dm 3 B 4 dm 3 C 6 dm 3 D 12 dm 3 3. Bri asia was inflating a soccer ball. She measured the radius initially to be 6 inches. What effect would inflating the ball to 12 inches have on the volume of the air inside the soccer ball? What is the ratio of the volume of the ball with less air to when it has more air? 4. A sphere has a diameter of 5 feet. If it is expanded to 2.5 times its diameter, what will be its change in volume? 5. 6. 7. Brendan and Rachel both had a rectangle in front of them. If Brendan s rectangle was 2 of Rachel s 3 rectangle, what is the ratio of area of Brendan s rectangle to Rachel s? [A] 2 [B] 4 [C] 4 8 [D] [E] None of these 3 6 9 27 8. The We-R-Tubes company has 2 similar but differently sized cylindrical tubes. The larger tube holds 125 cm 3 while the smaller tube can only hold 27 cm 3. Which statement correctly describes how a person could find the ratio of the areas of each circle of the cylinder? [A] Take the cube root of each volume to find the ratio of the areas. [B] Take the cube root of each volume then double it to find the ratio of the areas. [C] The ratio of the volume of the cylinders is equal to the ratio of the area of the circles. [D] Take the cube root of each volume then square it to find the ratio of the areas. 22
9. 10.. 11. 12. Describe the effect on the volume and surface area for the given figure. 13. Describe the effect on the volume and surface 14. Describe the effect on the volume and surface area for the given figure. area for the given figure. 15. A rectangular garden is 20 feet long and 30 feet wide. The owner decided to increase the garden by doubling the length but leaving the width the same. Which statement correctly describes what happened to the area of the garden? [A] The area of the garden stayed the same. [B] The area of the garden doubled. [C] The area of the garden tripled. [D] The area of the garden quadrupled. [E] The area can not be determined since only one side increased. 23
REVIEW 1) The drawing shows the top view of a structure built with cubes as well as the number of cubes in each column of the structure. Which 3-dimensional view represents the same structure? F G H J 2) How many faces, edges, and vertices are in each figure? Faces: Edges: Vertices: Faces: Edges: Vertices: 3) Match the nets with their corresponding solid. A. B. C. D. E. 24
#4-9: Find the lateral surface area, total surface area, and volume. ROUND ALL ANSWERS TO THE NEAREST TENTH. 4) 5) 5 in 12 cm 14 in. 2 in 4 cm *Shaded part is the base *Use 3.14 for Pi P = B= h= P = B= h= LSA = SA = V = LSA = SA = V = 6) 5 in 7) Regular hexagonal prism with apothem of 2 3 3 in 10 in 7 mm 4 mm P = B= h= P = B= h= LSA = SA = V = LSA = SA = V = 25
16 in 8) 9) 20 in 24 in LSA = SA = V = LSA = SA = V = 10) Given the following rectangular prism, answer the following questions about a similar prism in which the dimensions have been tripled. 4 ft 5 ft 12 ft a) What are the new dimensions?,, b) What is the new volume? V= c) The volume of the new prism is times larger than the volume of the original prism. 11) Disney wants to make a new version of Arial that is larger than the original. They now need to increase the dimensions of the old box by a factor of 2.5. If the old surface area was 838 in 2 and the old volume was 1463 in 3, to the nearest tenth what will be surface area and volume for the new box? 12) If the surface area of a cube is increased by a factor of 16, what is the change in the length of the sides of the cube? 26
13) A cube-shaped piece of playground equipment has a cylindrical portion removed, as shown in the diagram. The diameter of the opening is 5 feet. What is the approximate volume of the remaining portion of the cube? 6 ft 6 ft 6 ft 14) Write an equation to find the volume of the composite figure. Use the numbers in the given figure. 15) A company packages their product in two sizes of cylinders. Each dimension of the larger cylinder is three times the size of the corresponding dimension of the small cylinder. Based on this information, how much bigger is the larger cylinder s volume from the smaller cylinder s volume? r 3r h 3h 16) What is the best description of the solid figure shown? A a regular polygon B a convex polygon C a regular polyhedron D a nonregular polyhedron 4 4 4 27