# Thread: Volume bounded by cylinders (Multivar)

1. ## Volume bounded by cylinders (Multivar)

Find the volume bounded by the cylinders $x^2+y^2=r^2$ and $y^2+z^2=r^2$.

That's the full question, and I am confused because both of those equations would seem to form circles.

2. $V=\iint_{x^2+y^2\leq r^2} 2\sqrt{r^2-y^2} dxdy$

3. I have no idea what that means or where it came from.

4. have you learned the multiple integral part in calculus class?
please refer to the definition, and try you best to image the solid.

5. Yes, we have gone over multiple integrals and I understand that part of the notation, but little else.

1. Where did that integrand come from?
2. What does the $x^2+y^2\leq r^2$ region mean? I've looked over my past notes and there is definitely nothing like that in there.