a) Find the area of the circle formed when a sphere is cut by a plane at a distance y from the centre, where y > r.

I worked this out to be $\displaystyle \pi(r^2 - y^2)$.

b) By integration, prove that the volume of a 'cap' of height $\displaystyle \frac{1}{4}r$ from the top of the sphere is $\displaystyle \frac{{11\pi}r^3}{192}}$.

I'm not really sure what to do here. I can find the area of the circular base of the 'cap', but I don't know what to do with it.

Thanks.