Volume by disks, washers and shells

Spin a region around the x-axis and slice the solid into thin disks (or washers when there’s a hole). Add up the slices and the sum approaches the exact volume.

The region and its slices

The solid, built slice by slice

0/12
12
Slice at x =–
Outer radius R–
Inner radius r–
Slice volume–
Running total–
Exact volume–

The idea