Question

A cylinder has a height that is 2 times as large as its radius. The lateral area of the cylinder is 16π square units. What is the height of the cylinder?

Answer 1

$\bf \textit{lateral surface area of a cylinder}\\\\ LA=2\pi rh~~ \begin{cases} r=radius\\ h=height\\ -----\\ h=\stackrel{twice~r}{2r}\\ LA=16\pi \end{cases}\implies 16\pi =2\pi r(2r)\implies 16\pi =4\pi r^2 \\\\\\ \cfrac{16\pi }{4\pi }=r^2\implies 4=r^2\implies \sqrt{4}=r\implies 2=r$

and since h = 2r, well, you know what that is.