# Surface Area of a Cylinder

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 + 2B.  Since the base of a cylinder is a circle, we substitute 2πr for p and πr2 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. = 2πrh.

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. = 2π(3)(9) = 54π inches2

≈ 169.64 inches2

The general formula for the total surface area of a cylinder is T. S. A. = 2πrh + 2πr2.

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. = 2π(5)(7) + 2π(5)2 = 70π + 50π

= 120π inches2

≈ 376.99 inches2