Find Volume Inside x^2+y^2+z^2=4 and (x+2)^2+(y-1)^2+(z+2)^2=4

[real10]

x^2+y^2+z^2=4
(x+2)^2+(y-1)^2+(z+2)^2=4

find volume inside both.
thanks,

 

[balakrishnan_v]

Just draw and integrate.You will get
\frac{11 \pi}{12}

 

[real10]

i meant the volume of intersection due to those spheres.(common to both)
any details like what are the bounds for the integral u set up and which one..

thanks again,

 

[amcavoy]

I may be wrong, but try to find the region first by setting both equations equal. The "height" of each point in the intersection will be equal to the first equation minus the second.

z_1=\sqrt{2-x^2-y^2}

z_2=\sqrt{4-(x+2)^2-(y-1)^2}-2

V=\iint\limits_{D}\left(z_1-z_2\right)dA