Circumference = 2\(\pi\)r
If the circumference of the base of the cylinder is 16\(\pi\) then
16\(\pi\) = 2\(\pi\)r
Divide by 2 on both sides.
8\(\pi\) = \(\pi\)r
Divide by \(\pi\) on both sides.
8=r
So our radius is 8. So the height of the cylinder is 8/2 = 4.
The surface area of a cylinder is
\(SA=2\pi rh+2\pi r^2\)
Just plug in r as 8 and h as 4.
\(SA=2\pi (8)(4)+2\pi (8)^2\)
\(SA=2\pi 32+2\pi 64\)
\(SA=64\pi + 128\pi\)
\(SA=192\pi\)
The surface area is \({\boxed{192\pi}\).
