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
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
But now I'm guessing I need to set up a double integral. Looking at bounds, -2<x<2 and -1<y<1,
Is this the right way to go?
How then would I show it is given by the above integral?