1. A sphere with radius 2 (

) has its cylindrical core of radius 1 removed (

), what is the volume of the resultant solid?

a) Use cylindrical coordinates to find the volume of the resultant solid.

b) Use spherical coordinates to find the volume of the resultant solid.

For a) I just used cylindrical coordinates to find the volume of the cylinder, then used

which is the volume of the sphere then minus the volume of the cylinder from it.

For b) I used spherical coordinates to find the volume of the sphere, then used

which is the volume of the cylinder, then used the volume of sphere minus the volume of cylinder.

Now what I am wondering is... is that the right way to interpret the question? Or does the question mean use cylindrical coordinates ONLY to work out the volume? If so... how do I do that? Cause I thought as long as I

**used** cylindrical coordinates to find the volume that's fine.

Same goes for b)