# Math Help - Mass in a spherical shell

1. ## Mass in a spherical shell

Find the mass of the portion lying in the first octant of the spherical shell between the two spheres with radii a less than b if the density at point (x,y,z) is x. Thanks for anybody's help!

2. Originally Posted by nbram87
Find the mass of the portion lying in the first octant of the spherical shell between the two spheres with radii a less than b if the density at point (x,y,z) is x. Thanks for anybody's help!
Use spherical polars, then $x=\rho \sin(\phi)) \cos(\theta))$, so the required mass is:

$M=\int_V x ~dV=\int_{\rho=a}^b \int_{\phi=0}^{\pi/2} \int_{\theta=0}^{\pi/2} x~ \rho^2 \sin(\phi) d\rho~ d\phi~ d\theta$

RonL