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## Homework Statement

Am I going about this the right way?

There is a sphere of radius 3 and a region that lies between the planes [tex]z=1[/tex] and [tex]z=2[/tex] and has a density of [tex]cz[/tex]. We are asked to work in cylindrical coordinates.

## Homework Equations

Let [tex]\rho=\sqrt{9-z^2}[/tex], is the following the right formula?

[tex]I=\displaystyle{\int_R}cz\rho^2\,dV[/tex] where [tex]dV=\rho\,d\theta\,d\rho\,dz[/tex]

## The Attempt at a Solution

Would this be the integral?

[tex]I=2\pi c z\displaystyle{\int^2_1}\displaystyle{\int^{\sqrt{9-z^2}}_0}\rho^3\,d\rho\,dz[/tex]

Thanks