Frustum of a Cone

Frustum of a Cone

One of the two solids obtained by cutting a cone with a plane that is parallel to its base and that meets all its generatrices.

Of the two solids obtained, the one that does not contain the apex of the cone is called the “frustum of the cone;” the other solid is a cone.

Formulas

This illustration shows a right circular cone frustum with radii $$r_{1}$$ et $$r_{2}$$ and generatrices:
h = m $$\overline{O_{1}O_{2}}$$  and s = m $$\overline{P_{1}P_{2}}$$.

• The total area A of the frustum of a cone is given by: A = π ($$r_{1}+ r_{2}$$) s + π $$r_{1}^{2}$$ + π $$r_{2}^{2}$$.
• The volume V of the frustum of a cone is given by: V = $$\dfrac{πh}{3}$$ × ($$r_{1}^{2}$$ + $$r_{1}r_{2}$$ + $$r_{2}^{2}$$).