31. The volumes of two spheres are 729  in . 3 729 , in , . cubed  and 27  in . 3 . 27 , in , . cubed , .
    1. Find the ratio of their radii.
    2. Find the ratio of their surface areas.
32. The volumes of two similar pyramids are 1331  cm 3 1331 . cm cubed  and 2744  cm 3 . 2744 . cm cubed , .
    1. Find the ratio of their heights.
    2. Find the ratio of their surface areas.
33. A clown's face on a balloon is 4 in. tall when the balloon holds 108  in . 3 108 , in , . cubed  of air. How much air must the balloon hold for the face to be 8 in. tall?

Copy and complete the table for the similar solids.

38. Literature In Gulliver's Travels, by Jonathan Swift, Gulliver first traveled to Lilliput. The Lilliputian average height was one twelfth of Gulliver's height.
    1. How many Lilliputian coats could be made from the material in Gulliver's coat? (Hint: Use the ratio of surface areas.)
    2. How many Lilliputian meals would be needed to make a meal for Gulliver? (Hint: Use the ratio of volumes.)

C Challenge

39. Indirect Reasoning Some stories say that Paul Bunyan was ten times as tall as the average human. Assume that Paul Bunyan's bone structure was proportional to that of ordinary people.

    

    1. Strength of bones is proportional to the area of their cross section. How many times as strong as the average person's bones would Paul Bunyan's bones be?
    2. Weights of objects made of like material are proportional to their volumes. How many times the average person's weight would Paul Bunyan's weight be?
    3. Human leg bones can support about 6 times the average person's weight. Use your answers to parts (a) and (b) to explain why Paul Bunyan could not exist with a bone structure that was proportional to that of ordinary people.
40. Square pyramids A and B are similar. In pyramid A, each base edge is 12 cm. In pyramid B, each base edge is 3 cm and the volume is 6  cm 3 . 6 , cm cubed , .
    1. Find the volume of pyramid A.
    2. Find the ratio of the surface area of A to the surface area of B.
    3. Find the surface area of each pyramid.

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