- #1

- 9

- 0

## Homework Statement

Inside the sphere x

^{2}+ y

^{2}+ z

^{2}= R

^{2}and between the planes z = [tex]\frac{R}{2}[/tex] and z = R. Show in cylindrical and spherical coordinates.

## Homework Equations

[tex]\iiint\limits_Gr\,dz\,dr\,d\theta[/tex]

[tex]\iiint\limits_G\rho^{2}sin\,\theta\,d\rho\,d\phi\,d\theta[/tex]

## The Attempt at a Solution

[tex]2\int_0^{2\pi}\int_0^{R\sqrt{\frac{3}{4}}}\int_?^{\sqrt{R^{2}-r^{2}}}r\,dz\,dr\,d\theta[/tex]

Is my upper limit for r correct? How do I find the lower limit for z?

[tex]\int_0^{2\pi}\int_0^{\frac{\pi}{3}}\int_?^R\rho^{2}sin\,\theta\,d\rho\,d\phi\,d\theta[/tex]

How do I find the lower limit for rho?