A cone is placed inside a cylinder as shown. The radius of the cone is half the radius of the cylinder. The height of the cone is equal to the radius of the cylinder. What is the volume of the cone in terms of the radius, r?

Given:

Let us assume the radius of the cylinder is x.

radius of the cone is half the radius of the cylinder: x/2

height of the cone is equal to the radius of the cylinder: x

radius of cone: x/2; height of the cone: x

volume of the the cone = π r² h/3

V = 3.14 * (x/2) ² * x/3

V = 3.14 * x²/4 * x/3

V = (3.14 * x² * x) / 4*3

V = 3.14 x³ / 12