posted by Anonymous .
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
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.
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