You are told that the volume of an object of unknown shape is given by V equals where V is the volume and d is the diameter of the sphere?

Answer 1

The only shape whose volume could be determined by diameter alone is a sphere. The volume of a sphere is 4πr3/3. The radius of a sphere is half it's diameter, so you can say that given the diameter, d, the volume, v, can be determined with the equation:

v = 4π(d / 2)3 / 3

v = (4πd3 / 8) / 3

v = 4πd3 / 24

v = πd3 / 6