Question

The area of cross section of the cylinder is 32cm. How do I determine the total surface area?

Answer 1

Given the cross sectional area, CSA, of a cylinder to be

The cross section of a cylinder is a circle, thus the formula for the cross sectional area of a cylinder is

`\text{CSA}=\pi r^2`

Solving to find the radius of the cylinder below

`\begin{gathered} 32=\pi r^2 \\ \text{Divide both sides by }\pi \\ (\pi r^2)/(\pi)=(32)/(\pi) \\ r^2=(32)/(\pi) \\ \text{Square root of both sides} \\ \sqrt[]{r^2}=\sqrt[]{(32)/(\pi)} \\ r=\sqrt[]{(32)/(\pi)}cm \end{gathered}`

To find the total surface area, TSA, of a cylinder, the formula is

`\text{TSA}=2\pi rl+2\pi r^2`

Where

Subsitute the values intom the formula for the total surface area of a cylinder

`\begin{gathered} \text{TSA}=2\pi rl+2\pi r^2 \\ \text{TSA}=2(\pi*\sqrt[]{(32)/(\pi)}*25)+2(\pi*(\sqrt[]{(32)/(\pi)})^2) \\ \text{TSA}=501.3257+64 \\ \text{TSA}=565.3257 \\ \text{TSA}=565.3\text{cm}^2\text{ (nearest tenth)} \end{gathered}`

Hence, the total surface area of the cylinder is 565.3cm² (nearest tenth)