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I have been given the coordinates of a cylinder inside a sphere and want to convert to Cylindrical coordinates to compute the volume of the cylinder.

Can you please check the limits and integral I have?

The cylinder is x^2+y^2= 4

sphere = x^2+y^2+z^2= 9

As its a cylinder we have

Limits are 0<= theta <= 2\pi 0<= r <= 2 and

Inside a sphere with limits

sphere = x^2+y^2+z^2= 9

z = sqrt{9-r^2}

So would my integral be:

\int{{0}{2\pi} \int{0}{2} \int{0}{sqrt{9-r^2}} r dz dr d(theta)

regards