We will have the following:
[tex]\begin{gathered} 282.7in{}^3=\pi(5in)^2h\Rightarrow h=\frac{282.7in^3}{\pi25in^2} \\ \\ \Rightarrow h=3.599448193...in\Rightarrow h\approx3.6in \end{gathered}[/tex]
So, the height of the cylinder is approximately 3.6 in.
