It's much more impressive if you can show the answer is independent of the variables and then use the limiting case to find the answer. As another poster wrote,

It's much more impressive if you can show the answer is independent of the variables and then use the limiting case to find the answer. As another poster wrote, all you have to do is write down the integrals for the volumes and notice that in the difference the R^2 terms will cancel. Unfortunately, in this case the integrals are trivial to evaluate. I think a much more interesting problem would be one where the same approach I described works, except it's not tractable (or at least not easy) to do the integrals in your head.