Volume and surface area of the cone

The right cone is the second solid of revolution: it is generated by rotating a right triangle about one of its legs.

Property — Right cone

Right cone (from the rotation of a right triangle about a leg): base radius $r$, height $h$, slant height $\ell = \sqrt{r^2+h^2}$ (the hypotenuse of the triangle).

• $V = \tfrac{1}{3}\pi r^2 h$
• $S_{\text{lat}} = \pi r\ell$
• $S_{\text{tot}} = \pi r(r+\ell)$

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Topics: Synthetic geometry of space
Concepts: Apothem · Cone · Solids of revolution · Surface area · Volume
Skills: Using formulas