Derive the formula for the volume of the frustum of a cone.

Volume of a Frustum

The radii of the frustum of a right circular cone are in the ratio 2 : 1. What is the ratio of the volume of the frustum of the cone to that of the whole cone ?

Volume of frustum of right circular cone

If r_1 and r_2 denote the radii of the circular bases of the frustum of a cone such that r_1> r_2 , then write the ratio of the height of the cone of which the frustum is a part to the height of the frustum.

Derive the formula for the curved surface area and total surface area of the frustum of a cone.

The base radius and height of a cone is 5cm and 25 cm respectively. If the cone is cut parallel to its base at a height of h from the base. If the volume of this frustum is 110 cm3 . Find the radius of smaller cone?

If h is the height, I the slant height and r_(1), r_(2) radii of the circular bases of the frustum of a cone, then slant height of the frustum = sqrt(( r_(1) - r_(2))^(2) + h^(2)) . Height of the cone of which the frustum is a part = (h r_(1) /( r_(1) - r_(2) ).We have a bucket in the form of frustum of a cone in which h = 8 cm, r_(1) = 9 cm and r_(2) = 3 cm. Find its volume.