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1. The problem statement, all variables and given/known data

Find the volume between of the shape that is confined between the two cylinders and the xy-plane. Maybe I have understood it wrong, but after drawing them it looks like the intersection is a dome-looking shape. So I'm guessing the volume that I have to find is between the dome and the ground (xy-plane).

2. Relevant equations

The two cylinders

[itex]x^2 = 4 - 4z[/itex]

[itex]y^2 = 4 - 4z[/itex]

3. The attempt at a solution

I'm not sure how to do this. I know that [itex]x = y = +- 2[/itex] when [itex]z = 0[/itex] and [itex]x = y = 0[/itex] when [itex]z = 1[/itex].

I thought that maybe adding the two equations can give an equation for how z varies with x and y.

[itex]x^2 + y^2 = 8 - 8z[/itex] and then solve for z and take the integral of z.

In polar coordinates, the radius varies from 0 to 2. That gives me a volume of 3 pi.

The volume is supposed to be 8... any ideas?

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# Volume of dome -shape

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