5. What are Platonic Solids? Why are they called that? Bonus if you can get them all!
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1 Geometry Unit 9 Surface Area & Volume Test Good Luck To: Period: 1. Define polyhedron: 2. Define surface area: 3. Define volume: Classify the following as polyhedra or not. Circle yes or no. If you circle no, then explain why that figure is not a polyhedron. 4a. Cylinder 4b. Pyramid 4a. Yes or No 4b. Yes or No 5. What are Platonic Solids? Why are they called that? List them Bonus if you can get them all! 9. Is it possible for a polyhedron to have 6 faces, 6 vertices, and 6 edges? Why or why not? Geometry Unit 9 Test Surface Area & Volume Page 1 of 7
2 When we use the surface area and volume formulas studied in this chapter, we sometimes have a B in the formula. That stands for the area of the base. List 3 real-life examples of a geometric solid, tell which formula you would use (it has to be one of the formulas that has a B in it), and then identify the shape of the base for each of your examples. For instance: (You can t use this example by the way!) Real life example: The Luxor 1 Volume formula for a Pyramid is V = Bh 3 The shape of the base is a square, so in place of B I would use the area formula for a square which is 2 s. 10. Real life example: Surface Area or Volume formula for a is The shape of the base is a so in place of B I would use the area formula for a which is. 11. Real life example: Surface Area or Volume formula for a is Shape of the base is a so in place of B I would use the area formula for a which is. 12. Real life example: Surface Area or Volume formula for a is Shape of the base is a so in place of B I would use the area formula for a which is. 13. Find the surface area of the right prism. Surface area = 48 m 42 m 40 m Geometry Unit 9 Test Surface Area & Volume Page 2 of 7
3 14. Find the surface area and volume of the right cylinder below. (Leave your answer in terms of π.) 14. Surface Area = _ Volume = _ 15. Find the surface area and volume of the right cone below. (Round the result to one decimal place.) 15. Surface Area = Volume = 16. The pyramid below has a square base and a slant height of 7 ft. Find its surface area and volume. (If necessary, round your answer to one decimal place.) 16. Surface Area = Volume = 17. The top of the cylindrical container below has the shape of a hemisphere. The total volume of the container is. (Leave your answer in terms of π.) 17. Volume = 18. Find the diameter of a sphere that has a surface area of 64π. in Diameter = Geometry Unit 9 Test Surface Area & Volume Page 3 of 7
4 19. The shipping crates shown are similar. A. Find the similarity ratio of the crate on the left to the crate on the right. B. Find the ratio of their surface areas. C. Find the ratio of their volumes. 19. A. B. C An aquarium in a restaurant is a rectangular prism and measures 3.5 feet by 4 feet by 4 feet. If the optimum fish to water ratio is 1 fish to every 6 cubic feet of water, how many fish can the restaurant have? (Remember you can t have a partial fish so round correctly!) 20. (SE) 21. A cylindrical can has a volume of 12π cubic inches with a radius of 2 inches. How many inches tall is the cylindrical can? 21. A. 3 B. 6 C D Geometry Unit 9 Test Surface Area & Volume Page 4 of 7
5 (SE) 22. A regular pyramid has height of 6 inches and the measure of the base edge is 7 inches in. 7 in. What is the volume of the pyramid? A. 49 in. 3 B. 98 in. 3 C. 147 in. 3 D. 294 in. 3 (SE) 23. A group of students wants to make a fabric toy ball to donate to the canine rescue. The diameter of the ball is 3 inches. 23. A. 29 in. 2 B. 57 in. 2 C. 76 in. 2 D. 114 in. 2 Approximately how many square inches of fabric will they need for each ball? 2 (PE) 24. The formula for the volume of a cylinder is V = π r h. Given V and h, which formula would be used to find r? 24. A. r = πvh B. r = V π h C. r = πvh D. V r = π h Geometry Unit 9 Test Surface Area & Volume Page 5 of 7
6 (PE) 25. A cereal box is 18 inches by 3 inches by 12 inches. After breakfast, the box is one-third full. Volume = (Area of Base) height 25. How many cubic inches of cereal are left inside? A. 36 in. 3 B. 72 in. 3 C. 216 in. 3 D. 648 in. 3 (LTMR) 26. Use the dimensions given in the diagram below x 15 What is the value of x? A. 25 B. 21 C. 17 D. 8 Geometry Unit 9 Test Surface Area & Volume Page 6 of 7
7 (LTMR) 27. The following figures are similar. 27. W X 24 Z 48 Y A B 16 D 32 C What is the scale factor of WXYZ to ABCD? A. 3 to 2 B. 3 to 1 C. 4 to 3 D. 1 to 2 (LTMR) 28. Gina stands at the corner of the rectangular garden shown below. 28. D B 15 ft A 20 ft C How much shorter in feet is it to walk diagonally through the garden (A to B) instead of walking around its edge (A to C and C to B)? A. 5 ft B. 10 ft C. 15 ft D. 25 ft Geometry Unit 9 Test Surface Area & Volume Page 7 of 7
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