I need to find the volume of the intersection set $A\cap B$ whereby $A=\{(x,y,z)\in \mathbb{R}|{x}^{2}+{y}^{2}+{z}^{2}\le 1\}$ and $B=\{(x,y,z)\in \mathbb{R}|{x}^{2}+{y}^{2}\le 1/2\}.$

It is clear that $A$ represents the unit ball centered at the origin and $B$ represents the cylinder with radius $\frac{1}{\sqrt{2}}.$. I should at some point use the Fubini theorem. I am puzzled by intersection set. Can somebody provide a solution proposal or a comment? Thanks.

It is clear that $A$ represents the unit ball centered at the origin and $B$ represents the cylinder with radius $\frac{1}{\sqrt{2}}.$. I should at some point use the Fubini theorem. I am puzzled by intersection set. Can somebody provide a solution proposal or a comment? Thanks.