Thread: help with triple integral spherical coordinates

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.

Originally Posted by messianic

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.

If you look at the sphere from the top it's a circle of radius 1 and centered at . The values of for this is . If it was centerd at then it would be as you say.

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.