Calculate volume between two geometric figures I have a figure C that is defined as the intersection between the sphere $x^2+y^2+z^2 \le 1 $ and the cyllinder $x^2+y^2 \le \frac{1}{4}$.
How should i calculate the volume of this figure?

The given cylinder and the given sphere share the sections given by $z=\pm\frac{\sqrt{3}}{2}$. If $|z|\leq\frac{\sqrt{3}}{2}$, the area of the section is $\frac{\pi}{4}$. If $\frac{\sqrt{3}}{2}\leq|z|\leq 1$, the area of the section is $\pi(1-z^2)$.
Integrating $1$ on sections, we get that the volume is given by:
$$ \frac{\pi}{4}\sqrt{3}+2\pi\int_{\sqrt{3}/2}^{1}(1-z^2)\,dz =\color{red}{\frac{\pi}{6}(8-3\sqrt{3})}.$$
