Question

The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?

Answer 1

Volume = 4/3 π r^3.

Explanation:

The formula for the volume of the cone is:

V = 1/3 π r^2 h where r = the radius of the base and h = the height.

Now h = 2d where d is the diameter.

Diameter d = 2r so h = 2(2r) = 4r.

So, substituting for h in the formula for V:

V = 1/3 π r^2 (4r)

= 1/3 π 4r^3

= 4/3 π r^3.