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## Homework Statement

Use spherical coordinates to find the volume of the solid enclosed between the spheres $$x^2+y^2+z^2=4$$ and $$x^2+y^2+z^2=4z$$

## Homework Equations

$$z=\rho cos\phi$$ $$\rho^2=x^2+y^2+z^2$$ $$dxdydz = \rho^2sin\phi d\rho d\phi d\theta$$

## The Attempt at a Solution

The first sphere is a sphere of radius 2 centered at the origin, and the second is a sphere of radius 2 centered at (0,0,2). So I tried setting the up the triple integral as $$\int_{0}^{2\pi}\int_{0}^{\pi/2}\int_{4cos\phi}^{2} \rho^2sin\phi d\rho d\phi d\theta$$

Which gives me a negative answer. I'm guessing my bounds for phi or rho are off?

Additionally, the question suggests I use the iterated order $$d\phi d\rho d\theta$$ but I'm unsure how to change the iterated order around like it suggests. Any help would be appreciated, thanks!