Hi everyone, I need help with this task:

Find the volume of solid inside both of the spheres

$\displaystyle \rho = 2\sqrt{2} cos \phi $ and $\displaystyle \rho = 2$

thank you in advance for any help with this

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- Nov 25th 2007, 06:23 AMpearlmanVolume of solid inside 2 spheres
Hi everyone, I need help with this task:

Find the volume of solid inside both of the spheres

$\displaystyle \rho = 2\sqrt{2} cos \phi $ and $\displaystyle \rho = 2$

thank you in advance for any help with this - Nov 25th 2007, 06:33 AMtopsquark
- Nov 25th 2007, 01:17 PMgalactus
I believe it may be a sphere. Just not centered at the origin.

They intersect when $\displaystyle 2=2\sqrt{2}cos{\phi}$

$\displaystyle cos^{-1}(\frac{1}{\sqrt{2}})=\frac{\pi}{4}$

$\displaystyle \int_{0}^{2{\pi}}\int_{0}^{\frac{\pi}{4}}\int_{0}^ {2}{\rho}^{2}sin^{2}{\phi}d{\rho}d{\phi}d{\theta}$