To be honest, for both parts, my only idea so far would be to divide the rate expression by the sphere area and multiply by the new available areas (that of a circle for part a and that of many circles for part b). But if I do this, I will have an "a" parameter always, which makes no sense because it is representative only of the sphere. Any ideas on how to approach this? All help is greatly appreciated.
don't use the perfect square model. You will keep getting Pi but it's not a real life formulae only used for theory. Try to use a Cartesian graph but three dimensions to take into account curve flexibility. Integral calculus is similar too or better.