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?

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