Kloten skär varandra längs kurvan \(x^2+y^2=4,z=0\), så området kan definieras genom villkoren \(x^2+y^2\le 4\) och \(-1+\sqrt{5-x^2-y^2}\ge z\ge 1-\sqrt{5-x^2-y^2}\). Detta leder till trippelintegralen \[ V=\iiint_{B_1\cap B_2} 1\,dxdydz= \] \[ \iint_{x^2+y^2\le 4}\left(\int_{1-\sqrt{5-x^2-y^2}}^{-1+\sqrt{5-x^2-y^2}}dz\right)dxdy= \] \[ \iint_{x^2+y^2\le 4}\left(2\sqrt{5-x^2-y^2}-2\right)dxdy= \] \[ \int_0^{2\pi}d\theta \int_0^2\left(2\sqrt{5-r^2}-2\right)rdr= \] \[ 2\pi \Big[-\frac23(5-r^2)^{3/2}-r^2 \Big]_0^2= (20\sqrt5 -28)\frac{\pi}{3}. \]