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 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.=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 inches 2

                               169.64 inches 2

The general formula for the total surface area of a cylinder is T.S.A.=2πrh+2π 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.=2π(5)(7)+2π (5) 2 =120π inches 2 376.99 inches 2