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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 $p h$ and the total surface area is $p h + 2 B$ . 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 $L . S . A . = 2 π r h$ .

Example 1:

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

Math diagram

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

$\approx 169.64 {inches}^{2}$

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

Example 2:

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

Math diagram

$\begin{array}{l} T . S . A . = 2 π (5) (7) + 2 π {(5)}^{2} \\ = 120 π {inches}^{2} \\ \approx 376.99 {inches}^{2} \end{array}$