I'm in Chicago without a computer so this will be short and sweet since I'm typing with my thumbs.
First correct and non-anonymous comment wins access to the Math Guide.
Chris bought a pumpkin last year that had a diameter of 10 inches and yielded the PERFECT amount of toasted seeds. His pumpkin this year has a diameter of 13 inches. Pumpkin skins generally have a thickness of one tenth of the radius of the pumpkin. Assume pumpkins are spherical and that each pumpkin has roughly equal amounts of seeds by volume. What will be the ratio of the amount of seeds Chris gets this year to the amount of seeds he got last year?
UPDATE: Nice work, Edward. Solution below the cut.