Answer
$2.76m$
Work Step by Step
Assume the cylinder has a radius of $r$(m), its volume would be $v1=\pi r^2\times20$
and the cone volume $v2=\frac{1}{3}\pi r^2(2r)=\frac{2}{3}\pi r^3$
The known total volume can be expressed as $\frac{2}{3}\pi r^3+20\pi r^2=500\pi/3$
which give an equation $r^3+30r^2-250=0$
Solving the equation numerically gives $r=2.76m$