Task 509

The task

Cylinder $B$'s height is equal to the radius of cylinder $A$ and cylinder $B$'s radius is equal to the height $h$ of cylinder $A$. If the volume of cylinder $A$ is twice the volume of cylinder $B$, the volume of cylinder $A$ can be written as $N \pi h^3$ cubic units. What is the value of $N$? [asy] size(4cm,4cm); path a=(0,-1.2)..(-10,0)--(10,0)..cycle; path b=(17,-0.9)..(13,0)--(21,0)..cycle; path c=(0,1.2)..(-10,0)--(10,0)..cycle; path d=(17,0.9)..(13,0)--(21,0)..cycle; draw(c); draw(d); draw(shift((0,7))*a); draw(shift((0,7))*c); draw(shift((0,15))*b); draw(shift((0,15))*d); draw((-10,0)--(-10,7)); draw((10,0)--(10,7)); draw((13,0)--(13,15)); draw((21,0)--(21,15)); draw(a); draw(b); label("$A$",(0,9),N); label("$B$",(17,18),N); [/asy]