I have a wrong answer to this, I think: 5 pi / 12, which is less than half the volume of the unit sphere (details: 1/2 of the volume of the unit sphere is 1/2 of 4/3 pi r^3 for r=1 , or 2/3 pi, or 8/12 pi ... 5/12 pi is less than that). I believe it's wrong since the volume of the unit sphere displaced up by 1, minus any overlap with the unit sphere at the origin, is larger than the upper half of a unit sphere.

The calculation requested is: Find the volume of the solid E outside the sphere x^2+y^2+z^2 = 1 and inside the sphere x^2+y^2+(z-1)^2=1 [Hint: Use spherical coordinates].

Any help finding an approach with spherical coordinates?

Thanks for any guidance!