Surface Area and Volume of Pyramids
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1 Surface Area and Volume of Pyramids Problem Set For each pyramid, identify the variable that represents each of the following: A. Height B. Slant height C. Side length of base a d e y z b w v c x 2. k j n p m Answer the question. 4. Use the labeled square pyramid to write an expression for each measure. q t s p r A. What is the volume of the pyramid? B. What is the surface area of the pyramid? 1 of 7
2 Identify the vertex, base edges, lateral edges, and altitude of each pyramid. 5. A 6. A D F E B C I J H G F C B D E Find the slant height of each pyramid cm 24 km 24 cm 36 km Find the surface area of each regular pyramid m m 14 km 14.4 km 8 m 10.4 km 12 km 2 of 7
3 ft km 33.6 ft 22 km 10.4 ft 12 ft km m 30 m 18 mi m 20 m mi 12 cm 14.8 cm 20 m 8.66 cm 10 cm 14 m 3 of 7
4 17. A cm I H B G C D 4.8 cm E 4 cm F height = 18 yd 8 yd Find the volume of each pyramid. 19. The figure is a square pyramid. 21. The figure is a square pyramid. 20 cm 16.4 cm 14 cm 14 cm 12 cm 20. The base of the triangular pyramid is equilateral. 22. The figure is a regular hexagonal pyramid. 22 km 26 km 18 m 13.9 km 16 km 15.6 m height = 34 m 4 of 7
5 23. The figure is a square pyramid. 26. The figure is a rectangular pyramid. 18 in. 17 m 8 m 15 in. 24. The base is a regular octagon. 6 m 27. The figure is a square pyramid. 8.2 cm 6 cm 8 cm 28. The figure is a regular octagonal pyramid. 10 cm cm 34 cm 25. The base is a right triangle. 40 km 18.1 km 15 km 22 km 12 km 9 km 5 of 7
6 29. The figure is an oblique square pyramid. 30. The base is a regular pentagon. 18 m 40 cm height 8 m 5.5 m 24 cm Answer each question. 31. What is the surface area to volume ratio of the regular hexagonal pyramid shown here? 32. The main entrance to the Louvre Museum in Paris, France, is a square pyramid made entirely of glass. One side of the base is 35 meters and the height is 20.6 meters m 9 in. height = 28 in. 35 m A. What is the surface area of the Louvre Pyramid including its base? B. What is the volume of the space occupied by the Louvre Pyramid? C. The area of a pane of glass in the Louvre Pyramid is about 3 square meters. If the base is excluded, about how many panes does the pyramid have? 6 of 7
7 33. The Khafre Pyramid is one of the pyramids of the Giza complex in Egypt. When it was originally constructed, the base of the square pyramid was 704 feet on one side and 446 feet tall. 704 ft 446 ft A. What was the surface area of the Khafre Pyramid, including its base? B. What was the volume of the Khafre Pyramid? C. If the density of the rock used to build the pyramid is 169 pounds per cubic foot, what is the weight of the Khafre Pyramid? 34. The dormer shown here is constructed by combining a right triangular prism with an oblique triangular pyramid. Find the volume of the space the dormer occupies. 5 ft 2 ft 35. Damian s construction company is tiling the roof of a gazebo. The roof is in the shape of a regular hexagonal pyramid with an open bottom. The side lengths of the hexagonal base are 5 feet and the slant height is 7 feet. A. Explain why the surface area of the roof will not equal the surface area of a regular hexagonal pyramid with the same dimensions. B. Calculate the volume and surface area of the roof. C. Explain which calculation from Part B Damian would use to determine the number of tiles he needs. 3 ft 3 ft 3 ft 5 ft 7 of 7
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national assessment program literacy and numeracy NUMERACY calculator ALLOWED year 7 2011 0:40 SESSION 1 Time available for students to complete test: 40 minutes Use 2B or HB pencil only Australian Curriculum,
NON-CALCULATOR Page Page , 31
Math 7 Midterm Review Please Note: Some topics covered in semester 1 are not found in our textbook. Therefore, the following topics are NOT covered in this review guide but WILL be on the exam. Refer to