Hi.

I've been asked to find the volume of the region bounded by the 3 inequalities $\displaystyle x^2+y^2<r^2, \, x^2+z^2<r^2, \, y^2+z^2<r^2$. This is, three cylinders of radius r. Using a triple integral to find the body seems to be the 'natural way', but I can't see how to calculate

$\displaystyle \iiint \left[x^2+y^2<r^2, \, x^2+z^2<r^2, \, y^2+z^2<r^2 \right] \, dx \, dy \, dz$

Thanks!