Question

9. Sheila has sketched a net for a cylinder as shown below. or r= 3 in h= 7.5 in What is the closest to the total surface area of her cylinder?

Answer 1

To calculate the area of a cylinder you have to calculate three areas, one is the surface area and the other two are the areas corresponding to the top and bottom of the cylinder.

The surface area can be calculated as

`SurfaceA=2\pi rh`

Area of the top and bottom

`2\cdot A_{\text{circle}}=2\pi r^2`

The total area of the cylinder is the sum of these areas:

`A=2\pi rh+2\pi r^2`

For r=3in and h=7.5in the area is:

`\begin{gathered} A=2\pi(3)(7.5)+2\pi(3^2) \\ A=63\pi \\ A\cong197.92in^2 \end{gathered}`

The answer closest to the total surface area of the cylinder is 198in²