Volume: The Washer Method

The disk method can be extende to cover solids of revolution with holes by replacing the representative disk with a representative washer.

To see how this concept can be used to find the volume of a solid of revolution, consider a region bounded by an outer radius Ro(x) and an inner radius Ri(x).

V=

Here are examples which show how washers are adding up.

VolumeOfRevolution
(x^(1/2),x^2,0..1,'axis'=
'horizontal',
'distancefromaxis'=0,
'output'='plot');

VolumeOfRevolution
(x^(1/2),x^2,0..1,'axis'=
'horizontal',
'distancefromaxis'=0,
'output'='animation');