Answer
$$ \pi $$
Work Step by Step
Our aim is to integrate the integral as follows:
$$ Volume=(4) \times \int^{\pi/2}_0 \int^{1}_0 \int^{r^2+1}_{r^2} dz \space r \space dr \space d\theta \\=(4) \int^{\pi/2}_0 \int^1_0 r \space dr \space d\theta \\=(2) \times \int^{\pi/2}_0 (1) d\theta \\=\pi $$
