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
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
I believe it may be a sphere. Just not centered at the origin.
They intersect when $\displaystyle 2=2\sqrt{2}cos{\phi}$
$\displaystyle cos^{-1}(\frac{1}{\sqrt{2}})=\frac{\pi}{4}$
$\displaystyle \int_{0}^{2{\pi}}\int_{0}^{\frac{\pi}{4}}\int_{0}^ {2}{\rho}^{2}sin^{2}{\phi}d{\rho}d{\phi}d{\theta}$