The volume between two surfaces can be calculated by
`V=int int_D (z_(t o p)-z_(b o t)) dA`
Where `D` is the area contained by the boundary of the volume projected onto the xy-plane.
To find `D` we need to solve when they two surfaces meet. Solve for `z` on both equations and set them equal to each other.
We have `z=sqrt(x^2+y^2)`
Notice that the bottom half of the sphere `z=-sqrt(1-(x^2+y^2))` is irrelevant here because it does not intersect with the cone. The following condition is true to find the curve of intersection.
Switch to polar coordinates to simplify the...
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