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## Homework Statement

## Homework Statement

Suppose that a square hole with sides of length 2 is cut symmetrically through

the center of a sphere of radius 2. Show that the volume removed is given by

where

I'm not sure how to approach this, but I figure you can express the sphere in terms of f(x,y,z) = [itex]x^2+y^2+z^2=4[/itex]

then I express z in terms of x and y

[itex]\sqrt{4-y^2-x^2}[/itex]

But now I'm guessing I need to set up a double integral. Looking at bounds, -2<x<2 and -1<y<1,

[itex]\int_{-2}^{2}\int_{-1}^{1}y\sqrt{4-x^2-y^2}dydx[/itex]

Is this the right way to go?

How then would I show it is given by the above integral?