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## Homework Statement

Find the triple integral for the volume between a hemisphere centred at ##z=1## and cone with angle ##\alpha##.

## The Attempt at a Solution

What I tried to do first was to get the radius of the hemisphere in terms of the angle ##\alpha##. In this case the radius is ##\tan \alpha##. I already figured out this integral in cylindrical polar coordinates and Cartesian coordinates. I am having a lot of trouble with spherical coordinates. I am trying to get ##\rho## for the hemisphere by drawing the projection of the shape on the xz plane and trying to get a formula for a radial ray that hits the hemisphere. The formula for a circle that is shifted up by one is ##x^2+(z-1)^2=\tan^2 \alpha##, this is the part where I am stuck trying to find the equation for ##\rho## in terms of the angle ##\phi## of the radial ray. The limits for ##\theta## and ##\phi## are really easy, but again ##\rho## I just can't seem to get.