# Volume bounded by cylinders (Multivar)

• December 13th 2009, 09:08 PM
davesface
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.
• December 13th 2009, 09:36 PM
Shanks
$V=\iint_{x^2+y^2\leq r^2} 2\sqrt{r^2-y^2} dxdy$
• December 13th 2009, 09:39 PM
davesface
I have no idea what that means or where it came from.
• December 13th 2009, 09:48 PM
Shanks
have you learned the multiple integral part in calculus class?
please refer to the definition, and try you best to image the solid.
• December 13th 2009, 10:11 PM
davesface
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.