the volumes of two similar solids are 729m^3 and 125m^3. the surface area of the larger one is 324m^2. what is the surface area of the smaller one? A)500m^2 B) 56m^2 C)100m^2 D)200M^2

Question

the volumes of two similar solids are 729m^3 and 125m^3. the surface area of the larger one is 324m^2. what is the surface area of the smaller one? A)500m^2   B) 56m^2    C)100m^2  D)200M^2

anonymous · Answer

Volume ratios are cubes, area ratios are squares.

The ratio of the volumes are 729:125 = 9^3:5^3, so the ratio of the areas would be 9^2:5^2 = 81:25

81        324
---  = -----
25          x

81x = 8100

Solve for x.