Question

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

Answer 1

Let ABC be a cone. A frustum DECB is cut by a plane parallel to its base.

Let r₁ and r₂ be the radii of the ends of the frustum of the cone and h be the height of the frustum of the cone.

In ΔABG and ΔADF, DF||BG

∴ ΔABG ∼ ΔADF

Volume of frustum of cone = Volume of cone ABC − Volume of cone ADE