The total surface area of a crlinder is given by
[tex]TSA=2\pi rh+2\pi r^2[/tex]
Given that the area of the cylinder is [tex]96\pi\, in^2[/tex] and the radius is 4 in, then
[tex]96\pi=2\pi(4)h+2\pi(4)^2 \\ \\ =8\pi h+32\pi \\ \\ \Rightarrow96=8h+32 \\ \\ \Rightarrow8h=96-32=64 \\ \\ \Rightarrow h= \frac{64}{8} =8\, in[/tex]
Therefore, the height of the cylinder is 8 in.
