\frac V 2+2\cdot\frac 1 3\frac d 2\left(\frac d 2\right)^2\pi=\frac 1 3 d\cdot d^2\pi\Leftrightarrow \frac V 2+\frac{d^3\pi}{12}=\frac{d^3\pi}3\Leftrightarrow V=\frac{d^3\pi}2=\frac{(a\sqrt 2)^3\pi}2=a\pi\sqrt 2