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  1. #1
    Junior Member whytechocolate01's Avatar
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    The volumes of two similar pyramids are 27 and 64. If the smaller has lateral area of 18, find the lateral area of the larger. Please explain. Thank you.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by whytechocolate01 View Post
    The volumes of two similar pyramids are 27 and 64. If the smaller has lateral area of 18, find the lateral area of the larger. Please explain. Thank you.
    The volumes of two similar solids are the the proportion of the cubes of
    corresponding linear measures (sides in this case).

    The lateral areas of two similar solids are the the proportion of the squares of
    corresponding linear measures (sides in this case).

    l1^3:l2^3 = 27:64

    and we want:

    l1^2:l2^2 = 27^{2/3}:64^{2/3} = 9:16

    Therefor if the smaller lateral area is 18, the larger is (18/9)*16 = 32

    RonL
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