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

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

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- Dec 13th 2009, 09:08 PMdavesfaceVolume bounded by cylinders (Multivar)
Find the volume bounded by the cylinders $\displaystyle x^2+y^2=r^2$ and $\displaystyle y^2+z^2=r^2$.

That's the full question, and I am confused because both of those equations would seem to form circles. - Dec 13th 2009, 09:36 PMShanks
$\displaystyle V=\iint_{x^2+y^2\leq r^2} 2\sqrt{r^2-y^2} dxdy$

- Dec 13th 2009, 09:39 PMdavesface
I have no idea what that means or where it came from.

- Dec 13th 2009, 09:48 PMShanks
have you learned the multiple integral part in calculus class?

please refer to the definition, and try you best to image the solid. - Dec 13th 2009, 10:11 PMdavesface
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 $\displaystyle x^2+y^2\leq r^2$ region mean? I've looked over my past notes and there is definitely nothing like that in there.