Question

Find the total surface area

Answer 1

The total surface area of the cylinder is approximately
`\( 653.54 \, \text{m}^2 \).`

The curved surface area (CSA) of a cylinder is given by the formula
`\( CSA = 2\pi r h \)`, where r is the radius and h is the height (or length in this case).

In this problem, you are given
`\( CSA = 546\pi \) and \( h = 21 \).`

`\[ 546\pi = 2\pi r * 21 \]`

Now, solve for r:

`\[ r = (546\pi)/(2\pi * 21) \]`

`\[ r = (546)/(42) \]`

`\[ r = 13 \, \text{m} \]`

Now, to find the total surface area (TSA) of the cylinder, we use the formula
`\( TSA = 2\pi r (r + h) \):`

`\[ TSA = 2\pi * 13 * (13 + 21) \]`

`\[ TSA = 2\pi * 13 * 34 \]`

`\[ TSA \approx 653.54 \, \text{m}^2 \]`

Therefore, the total surface area of the cylinder is approximately
`\( 653.54 \, \text{m}^2 \).`