# triple integrals

• March 4th 2009, 01:19 PM
sonia1
triple integrals
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: $p(x,y,z)=|z|$
• March 4th 2009, 05:49 PM
HallsofIvy
Quote:

Originally Posted by sonia1
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: $p(x,y,z)=|z|$

That is, of course, $\int\int\int_R |z| dV$, where R is the sphere of radius 3. If you use spherical coordinates, $z= \rho cos(\phi)$. You will want to use that for $0\le \phi\le \pi/2$ and $-\rho cos(\phi)$ for $\pi/2\le \phi\le \pi/3$.
• March 4th 2009, 11:20 PM
sonia1
oh sorry it's meant to be 2|z|..but i still don't understand the bit $-pcos(phi)$

so what would we integrate in terms of sperical coordinates