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math

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The areas of the faces of a rectangular box are 48 m2, 96 m2, and 288 m2.
A second box is cubical and each of its faces has area 16 m2.
Find the ratio of the volume of the first box to the volume of the second box.

  • math - ,

    let the sides of the first box be
    a, b , and c m
    so
    ab = 48 #1
    ac = 96 #2
    bc = 288 #3

    divide #1 by #2 --> b/c = 1/2 or c = 2b
    divide #2 by #3 --> a/b = 1/3 or b = 3a
    divide #1 by #3 --> a/c = 1/6 or c = 6a

    we know ab = 48
    a(3a) = 48
    3a^2 = 48
    a^2 = 16
    a = 4
    then b = 12
    and c = 24

    the volume of the first box must be
    4x12x24 or 1152 m^3

    the second box must have each side as 4 m
    so its volume is 4x4x4 = 64 m^3

    so the ratio of theri volumes = 1152:64
    = 18:1

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