Given rectangular prism A is similar to rectangular prism B and the volume of A is 125 ft3 and the volume of B is 27 ft3. What is the ratio of the surface areas for A:B?

Question

A. 3 : 5
B. 5 : 3
C. 25 : 9
D. 125. 27

Answer 1

Volumes of similar shapes are proportional to the cubes of their sides
so the sides are 5 : 3 (-----> since 5^3 : 3^3 = 125 : 27)
the surfaces areas of similar shapes are proportional to the squares of their sides

so 5:3 -----> 25 : 9