I have to calculate the volume of intersection of a sphere and a cylinder. The cylinder's radius is $r$ and the center point is $(r,0,0)$. The sphere's center point is $(0,0,0)$ and the radius $2r$.
I calculated the estimated volume with Monte Carlo methods but now I have to calculate the real volume with a formula. Is there any kind of explicit equation for this volume?
I will appreciate any kind of help!
Yes, draw a figure, and you will realize that the volume is given by $$ 2\iint_D \sqrt{(2r)^2-x^2-y^2}\,dx\,dy $$ where $$ D=\{(x,y)\in\mathbb R^2~|~(x-r)^2+y^2\leq r^2\}. $$ I leave it to you to calculate the integral.