The volumes of two similar figures are given. The surface area of the smaller figure is given. Find the surface area of the larger figure.

18. V = 27  in . 3 v equals . 27 , in , . cubed

    V = 125  in . 3 v equals . 125 , in , . cubed

    S . A . = 63  in . 2 cap s . cap a . equals . 63 , in , . squared

19. V = 27  m 3 v equals . 27 , m cubed

    V = 64  m 3 v equals . 64 , m cubed

    S . A . = 63  m 2 cap s . cap a . equals . 63 , m squared

20. V = 2  yd 3 v equals 2 . yd cubed

    V = 250  yd 3 v equals 250 . yd cubed

    S . A . = 13  yd 2 cap s . cap a . equals 13 . yd squared

See Problem 4.

21. Packaging There are 750 toothpicks in a regular-sized box. If a jumbo box is made by doubling all the dimensions of the regular-sized box, how many toothpicks will the jumbo box hold?
22. Packaging A cylinder with a 4-in. diameter and a 6-in. height holds 1 lb of oatmeal. To the nearest ounce, how much oatmeal will a similar 10-in.-high cylinder hold? (Hint: 1  lb  = 16  oz  1 , lb , equals 16 , oz )
23. Compare and Contrast A regular pentagonal prism has 9-cm base edges. A larger, similar prism of the same material has 36-cm base edges. How does each indicated measurement for the larger prism compare to the same measurement for the smaller prism?
    1. the volume
    2. the weight

B Apply

24. Two similar prisms have heights 4 cm and 10 cm.
    1. What is their scale factor?
    2. What is the ratio of their surface areas?
    3. What is the ratio of their volumes?
25. Think About a Plan A company announced that it had developed the technology to reduce the size of its atomic clock, which is used in electronic devices that transmit data. The company claims that the smaller clock will be similar to the existing clock made of the same material. The dimensions of the smaller clock will be 1 10 1 tenth  the dimensions of the company's existing atomic clocks, and it will be 1 100 1 100th  the weight. Do these ratios make sense? Explain.
    • What is the scale factor of the smaller clock to the larger clock?
    • How are the weights of the two objects related to their scale factor?

26. Reasoning Is there a value of x for which the rectangular prisms below are similar? Explain.

    

27. The volume of a spherical balloon with radius 3.1 cm is about 125  cm 3 . 125 . cm cubed , .  Estimate the volume of a similar balloon with radius 6.2 cm.
28. Writing Are all spheres similar? Explain.
29. Reasoning A carpenter is making a blanket chest based on an antique chest. Both chests have the shape of a rectangular prism. The length, width, and height of the new chest will all be 4 in. greater than the respective dimensions of the antique. Will the chests be similar? Explain.
30. Two similar pyramids have lateral area 20  ft 2 20 , ft squared  and 45  ft 2 . 45 . ft squared , .  The volume of the smaller pyramid is 8 ft 3 . 8 , ft cubed , .  Find the volume of the larger pyramid.

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