The **total **surface area of a cone is the sum of the area of its base and the lateral (side) surface.

The **lateral surface area **of a cone is the area of the lateral or side surface only.

Since a cone is closely related to a pyramid, the formulas for their surface areas are related.

Remember, the formulas for the lateral surface area of a pyramid is and the total surface area is .

Since the base of a cone is a circle, we substitute 2π*r* for *p* and π*r*^{2} for *B* where *r* is the radius of the base of the cylinder.

So, the formula for the **lateral surface area** of a right cone is *L. S. A. = *π*rl*, where *l* is the slant height of the cone*.*

**Example 1:**

Find the lateral surface area of a right cone if the radius is 4 cm and the slant height is 5 cm.

*L. S. A. = *π(4)(5) = 20π ≈ 62.82 cm^{2}

The formula for the **total surface area **of a right cone is *T. S. A. = *π*rl* + π*r*^{2}.

**Example 2:**

Find the total surface area of a right cone if the radius is 6 inches and the slant height is 10 inches.

*T. S. A. = *π(6)(10) + π(6)^{2}

= 60π + 36π

= 96π inches^{2}

≈ 301.59 inches^{2}