Question

Find the surface area of a cylinder with a base radius of and a height of .Write your answer in terms of , and be sure to include the correct unit.

Answer 1

We need to find the surface area of the given cylinder.

The surface area of a cylinder is the sum of the areas of the top and bottom bases and of the lateral surface.

The areas of the bases of a cylinder with radius r are, each, given by:

`\pi r²`

And the area of the lateral surface of a cylinder with a radius r and a height h is given by:

`2\pi rh`

Thus, the total surface area of a cylinder is:

`\pi r²+\pi r²+2\pi rh=2\pi r(r+h)`

In this problem, we have:

`\begin{gathered} r=2\text{ cm} \\ \\ h=7\text{ cm} \end{gathered}`

Thus, the surface area is given by:

Answer: 36π cm²