# geometry

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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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