Calculate the mass of a spherical bead of radius 3, centered at the origin, if the density of the material it is made of, is given by the function: $\displaystyle p(x,y,z)=|z|$
That is, of course, $\displaystyle \int\int\int_R |z| dV$, where R is the sphere of radius 3. If you use spherical coordinates, $\displaystyle z= \rho cos(\phi)$. You will want to use that for $\displaystyle 0\le \phi\le \pi/2$ and $\displaystyle -\rho cos(\phi)$ for $\displaystyle \pi/2\le \phi\le \pi/3$.