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March 30, 2017

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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.
V = 5 in3
V = 40 in3
S.A. = 4 in2

  • geometry - ,

    since their volumes are in the ratio of 2^3:1, their areas are in the ratio of 2^2:1.

    The larger figure has 4 times the area of the smaller one.

  • geometry - ,

    volume is proportional to the cube of a linear dimension
    Area is proportional to the square of a linear dimension

    The ratio of the volumes is 40/5 or 8

    That means the linear dimensions have the ratio of ∛8 or 2

    That means the areas have the ratio of 2² or 4

    so the area of the larger s 4 x 4 in² = 16 in²

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