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 .

b) By integration, prove that the volume of a 'cap' of height from the top of the sphere is .

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.