Question

The diagram shows part of the curve y=(1+4x)^
1/2 and a point P (6,5
) lying on the curve. The line PQ intersects the x-axis at Q (8,0)
.

(i) Find, showing all necessary working, the exact volume of revolution obtained when the shaded region is rotated through 360° about the x-axis. [7]
[In part (i) you may find it useful to apply the fact that the volume, V, of a cone of base radius r and vertical height h, is given by V =1/3 π r^2 h.]