The volume (v) of a sphere varies directly with the cube of its radius (r). if k is the constant of proportionally, which is the formula for this relationship?

This should be relatively easy, since most of us have learned and used the formula for the volume of a sphere:  V = (4/3)* pi* r^3.

Just combine (4/3)pi into a single value, k, which results in   V = kr^3.