Step 1: Write out the formula
[tex]\begin{gathered} SA=2\pi r(r+h) \\ \text{ Where } \\ r=\text{ the radius of the cylinder} \\ h=\text{ the height of the cylinder} \\ SA=\text{ the surface area} \end{gathered}[/tex]Step 2: Write out the values and substitute them into the formula
[tex]\begin{gathered} r=4in,SA=96\pi \\ \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} 96\pi=2\pi(4)(4+h) \\ 96=2(4)(4+h) \\ 4+h=\frac{96}{8} \\ 4+h=12 \\ h=12-4=8in \end{gathered}[/tex]Hence, the height is 8 inches
