Let a (cm) be the radius of the base of the cylinder, then 4a is the height of the cylinder. We have :

\(2\pi a\left(a+4a\right)=160\pi\Leftrightarrow5a^2=80\Leftrightarrow a^2=16\Leftrightarrow a=4\Leftrightarrow4a=16\)

The answer is : \(a^2\pi.4a=16\pi.16=256\pi\) (cm³)