The ratio of the radii of two spheres is 3: 1. the volume of the larger sphere is 729 in3. what is the volume of the smaller sphere?

Volume of sphere = 4/3 * π * r^3.

The constants don't matter because we're doing it by ratio, what matters is that volume is proportional to r^3. The radius is 3x larger, so the volume will be 3^3 = 27 times larger.

Therefore the volume of the smaller sphere is 729 / 27 = 27 in^3.