24. Writing Explain why the altitude P T ¯ p t bar in the pyramid below must be shorter than all of the lateral edges P A ¯ , P B ¯ , P C ¯ , p eh bar , comma , p b bar , comma , p c bar , comma and P D ¯ . p d bar , .

    

25. Think About a Plan The lateral area of a pyramid with a square base is 240   ft 2 . 240 , ft squared , . Its base edges are 12 ft long. Find the height of the pyramid.
    • What additional information do you know about the pyramid based on the given information?
    • How can a diagram help you identify what you need to find?

Find the surface area to the nearest whole number.

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29. Open-Ended Draw a square pyramid with a lateral area of 48   cm 2 . 48 , cm squared , . Label its dimensions. Then find its surface area.
30. Architecture The roof of a tower in a castle is shaped like a cone. The height of the roof is 30 ft and the radius of the base is 15 ft. What is the lateral area of the roof? Round your answer to the nearest tenth.

31. Reasoning The figure below shows two glass cones inside a cylinder. Which has a greater surface area, the two cones or the cylinder? Explain.

    

32. Writing You can use the formula S.A. = ( l + r ) r π cap s.cap a. , equals , open l plus , r close r pi to find the surface area of a cone. Explain why this formula works. Also, explain why you may prefer to use this formula when finding surface area with a calculator.
33. Find a formula for each of the following.
    1. the slant height of a cone in terms of the surface area and radius
    2. the radius of a cone in terms of the surface area and slant height

The length of a side (s) of the base, slant height (l), height (h), lateral area (L.A.), and surface area (S.A.) are measurements of a square pyramid. Given two of the measurements, find the other three to the nearest tenth.

34. s = 3  in. , S.A. = 39  in . 2 s equals 3 . in. , comma , cap s.cap a. , equals . 39 , in , . squared
35. h = 8  m , l = 10  m h equals 8 , m comma , l equals 10 , m
36. L.A. = 118   cm 2 , S.A. = 182   cm 2 cap l.cap a. . equals 118 , , cm squared , comma . cap s.cap a. . equals 182 , , cm squared

Visualization Suppose you revolve the plane region completely about the given line to sweep out a solid of revolution. Describe the solid. Then find its surface area in terms of π . pi .

37. the y-axis
38. the x-axis

C Challenge

39. the line x = 4 x equals 4
40. the line y = 3 y equals 3

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