Since a cylinder is closely related to a prism, the formulas for their surface areas are related.

Remember the formulas for the lateral surface area of a prism is *ph* and the total surface area is *ph + *2*B*. Since the base of a cylinder is a circle, we substitute 2*π**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 cylinder is *L. S. A. = *2*π**rh.*

**Example 1:**

Find the lateral surface area of a cylinder with a base radius of 3 inches and a height of 9 inches.

*L. S. A. = *2*π*(3)(9) = 54*π* inches^{2}

≈ 169.64 inches^{2}

The general formula for the **total surface area** of a cylinder is *T. S. A. = *2*π**rh* + 2*π**r*^{2}.

**Example 2:**

Find the total surface area of a cylinder with a base radius of 5 inches and a height of 7 inches.

*T. S. A. =* 2*π*(5)(7) + 2*π*(5)^{2} = 70*π* + 50*π*

= 120*π* inches^{2}

≈ 376.99 inches^{2}