Question

A sphere with a radius of 6 cm has the same volume as a cone with a height of 6 cm. What is the radius of the cone?

Answer 1

The volume of a sphere is
V_s = 4/3 * pi * r_s^3
The volume of a cone is
V_c = 1/3 * pi * h * r_c^2

Since we know that the two volumes are equal, we can say
V_s = V_c
4/3 * pi * r_s^3 = 1/3 * pi * h * r_c^2

Let us now isolate r_c, the radius of the cone:
4/3*r_s^3 = 1/3 *h*r_c^2
sqrt((4*r_s^3)/h) =r_c = 12 cm 

So the radius of the cone is 12 cm