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