Set up a triple integral that represents the volume of part of the ball x^2 + (y-1)^2 + z^2 </= 1 that is outside the cone rho = pi/6 and inside the cone rho = pi/3
In the answer, the dTheta part of the triple integral goes from 0 to pi. My question is how do you find that? Normally theta goes from 0 to 2pi.
Perhaps I'm missing something, but cones in spherical coordinates are usually given by and not . If the question was find the volume between the two cones , and the sphere , then that looks pretty tough to me. It's the part of the sphere in the plot below between the two cones. Note a small part of the sphere goes through the smaller cone so would have to take that into account. Maybe though this isn't what you want.