Geometry: ratios with volume

Question

The surface areas of two similar solids are 245m^2 and 605m^2. The volume of the larger one is 1331m^2. What is the volume of the smaller one?

Answer 1

Let k = the scale factor from the smaller to the larger solid. The ratio of the surface areas is k² and the ratio of the volumes is k³. So:

245/605 = k²

(245/605)^1/2 = k

Let x = the smaller volume:

x/1331 = k³ = (245/605)^3/2

Solve for x. Use your calculator to do the calculations. The units are m³.