Two spheres have surface areas of 100π units2 and 36π units2. If the volume of the larger sphere is π units3,

Scale Factor = 5/3

Radius of Smaller Sphere = 3 units

Radius of Larger Sphere = 5 units

Volume of Smaller Sphere = 36 π units^3

Just did the assignment.

In two solids, if the scale factor (ratio) of a linear dimension (edge length, diameter, perimeter, etc. is k, then the ratio of the areas is k^2, and the ratio of the volumes is k^3.

You have two solids with a ratio of areas of (100pi) / (36pi) which is a ratio of 100/36. This is the square of the ratio of the diameters, so the ratio of the diameters is 10/6. Then the ratio of the volumes is 10^3/6^3 = 1000/216.

If the larger sphere has volume pi units^3, then the volume of the smaller sphere is 216/1000 = 108/500 = 54/250 = 27/125 times the volume of the larger sphere.

The volume of the smaller sphere is 27pi/125 units^3