*r*and centre

*O*. The circle meets the positive x-axis at

**The point**

*B.**is on the interval OB. A vertical line through*

**A***A*meets the circle at

*P*. Let Theta=angle

*OPA.*

The shaded region bounded by the arc PB and intervals AB and AP is rotated about the x-axis. Show that the volume V formed is given by

V= ((π r^3)/3)(2 - 3sin Θ + sin^3 Θ)

Having a bit of trouble with this one. I've tried to find A in terms of theta (using trig) for the definite integral but have come upon nothing. I'm sure there's probably a key rule or identity or something which I'm missing, either that or I've interpreted the sketch wrong. Maybe I'm just too sleepy. Any help is appreciated thank you