Question

Applications of Integration:

Problem: 4B-2 Find the volume of the solid of revolution generated by rotating the regions
in 4B-1 around the y-axis.
PROBLEM e)

Solution: http://goo.gl/uSt4W (Problem e)

I can't seem to get my head around the integral.
I understand how we solved for y.
But what do the 2 parts in the integral represent?

Answer 1

More specific:
In this case is \[\pi(1-\sqrt{1-y}^2\]
equal to Region A and
\[\pi(1+\sqrt{1-y}^2\]
equal to Region B?