Here is the area to be revolved.  When revolved about the x-axis 
a pulley will be created with no hole for an axle.



The vertical elements all have one end on the same graph (the x-axis)
and the other end on the same graph (the parabola).  We could not say the
same if we used horizontal elements.  

We can do it this way:

Volume =  =  =  =  =

But because of symmetry w/r the y-axis we can just find the volume 
of the right side of the pulley and double it, and take the lower limit 
as 0 instead of -1.

 =

 =

 =

 -  =



 =

 =



Edwin