Volume of solid inside 2 spheres

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November 25th 2007, 06:23 AM
pearlman

Volume of solid inside 2 spheres

Hi everyone, I need help with this task:
Find the volume of solid inside both of the spheres
$\rho = 2\sqrt{2} cos \phi$ and $\rho = 2$

thank you in advance for any help with this
November 25th 2007, 06:33 AM
topsquark

Quote:

Originally Posted by pearlman

Hi everyone, I need help with this task:
Find the volume of solid inside both of the spheres
$\rho = 2\sqrt{2} cos \phi and \rho = 2$

thank you in advance for any help with this

Not that I'm good at answering these in any case, but I note that $\rho = 2\sqrt{2} cos(\phi)$ is not a sphere.

-Dan
November 25th 2007, 01:17 PM
galactus

I believe it may be a sphere. Just not centered at the origin.

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

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

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

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