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?

The volume of a cone  is 1/3 pi R^2 H    where R = radius of the base of the cone and hH= height of the cone

her H = r and R  = 0.5r  so the volume of the cone is
  1/3 * pi * (0.5r)^2 * r

  = 1/3 * pi *  0.25 r^3

= (1/12) pi r^3      Answer