CIE Math Pure math May/jun 2010 Variant 13.
Q9.
How do you find the volume??
Where is the cylinder 
I get how to find volume by integration..and put limits and stuff.
How do you know that when to subtract from something else.
A cylinder is formed when the line y=5 is rotated 360
o about the x-axis.
When you find volume by integration with the suitable limits, you'll get the volume
under the curve being rotated 360
o.
Volume of shaded region when rotated 360
o will be a small part of the big cylinder formed and you'll observe that the shaded region is above the curve.
Hence volume of Shaded region will be volume of cylinder minus volume under the curve
Volume of shaded region = Volume of cylinder - Volume under curve
Hope it helps
