Math Poblem

A volume of revolution is formed when part of a curve is rotated about a straight line.

 

Let F[x] be a particular quadratic curve. When x=1, F has gradient -2 and when x=2 F has gradient 0 and value 0.

 

Now the curve F[x] for x=0..2 is used as the model in a lathe to cut a cone of metal with a concave surface.

 

Given that the diameter of the material used is 8/sqrt(Pi) and the length of the material used is 2 (ie unequal scalings), what is the volume of material that is used in the cone ?

 

Additional Notes

 

Some clarification of this problem, with a somewhat crap diagram by me using Maple.... (believe me the curve goes all the way to x=2... now what is its volume ?

Done