#### Answer

$r\sqrt 2/\pi(r+2)$

#### Work Step by Step

volume of cylinder: $V = \pi*r^2*h$
volume of cube: $V=w*l*h$
$V_{cylinder} = \pi*r^2*h$
$V_{cylinder} = \pi*r^2*(2r+4)$
$V_{cube} = r\sqrt 2*r\sqrt 2*r\sqrt 2$
$V_{cube} = 2r^3\sqrt 2$
$V_{cube}/V_{cylinder} = 2r^3\sqrt 2/\pi*r^2*(2r+4)$
$V = 2r^3\sqrt 2/\pi*r^2*(2r+4)$
$V=2r\sqrt 2/\pi*(2r+4)$
$V=2r\sqrt 2/\pi*2(r+2)$
$V=r\sqrt 2/\pi(r+2)$