The ratio of the surface area of two spheres is 3:2. The volume of the larger sphere is 2,916 in3. What is the volume of the smaller sphere?

If the ratio of the radii of the two spheres is the square root of the given ratio of their surface area. That is, the ratio of the radii is sqrt 3: sqrt 2. The ratio of their volumes, on the other hand, is the cube of the ratio of their radii. That is 3^3/2 : 2^3/2. Letting x be the volume of the smaller sphere, the proportion becomes,

3^3/2 / 2^3/2 = 2,916 / x

The volume of the smaller sphere is approximately 1,587.27.