Question

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 6.
y = 6 − x
y = 0
y = 5
x = 0

Answer 1

You can use shells:

The region has to be broken up into the constant-height region where 0<=x<=1 and the slanting region where 1<=x<=6:

V = 2pi*Int(r*5 dx)[0,1] + 2pi*Int(rh dx)[1,6]
where r = 6-x
h = 6-x
= 138 2/3 pi

Or, using discs,

V = pi*Int(6^2 - y^2) dy[0,5]
= 138 2/3 pi