The volume of a cone varies jointly as the square of its rad

The volume of a cone varies jointly as the square of its radius and its height. If the volume of a cone is 18pi cubic inches when the radius is 3 inches and the height is 6 inches, find the volume of a cone when the radius is 2 inches and the height is 3 inches. The volume is in^3.

Solution

volume of cone varies with square of radius and its height

So, we can write V = kr^2*h where r is radius and h is height

Now V2/V1 = r2^2*h2/r1^2*h1 = (2)^2(3)/(3)^2(6)

v2 = V1((4*3/9*6) = 2V1/9 = 2*18pi/9 = 4pi