Let the radius and height of right circular cylinder be r and h respectively. Let radius of sphere is R. The radius of the cylinder and the diameter of the sphere are equal. Therefore, r = 2R The volumes of a right circular cylinder and a sphere are equal. => $$pi r^2h = frac{4}{3} pi R^3$$ => $$3 r^2h = 4(frac{r}{2})^3$$ => $$6 r^2h = r^3$$ => $$6h = r$$ => $$frac{h}{r} = frac{1}{6}$$