The volume of a cone varies jointly as the square of its radius and its height.

Question

If the volume of a cone is 12(pi) cubic inches when the radius is 2 inches and the height is 9 inches, find the volume of a cone when the radius is 3 inches and the height is 6 inches.

express your answer in terms of pi

Answer 1

The volume for a right circular cone is given by V = (pi)r²h/3

We want the volume when r is 3 and h is 6:

V = (pi)(9)(6)/3 = 18(pi) cu in

Answer 2

The formula for the volume of a cone:

V =Πr²h/3

This cone has a volume of 12Π when r=2 and h=9:

V = Π(2)²(9)/3

V = 12Π

Check !

Fin the volume when r=3 and h=6:

V = Π(3)²(6)/3

V = Π(9)(2)

V = 18Π cubic inches