




Calculate the volume generate by rotating the area A: around the yaxis.
Rotate the area
By rotating the area A, we generate a solid of revolution whose volume can be calculated using the shell method.
Shell method
We revolve around the yaxis a thin vertical strip of height y and width dx.
This generates a thinwalled cylindrical shell whose volume is dV.
dV is the area of the inner surface (2pxy) times the thickness of the wall (dx).
Volume of the torus
We get the volume of the solid of revolution by filling it with a very large number of very thin concentric shells, that is by integrating dV from 0 to 1.