How to Find the Volume of a Hershey's Brand Chocolate Kiss in Order to Win a Contest

Languishing in a postal line that was moving at glacial speed, my farsighted eyes read the small sign on the counter of the post office. The sign had a picture of the 100th Anniversary Stamp depicting a Hershey's Kiss stamp as part of the Postal Service's "Love and Kisses" stamp series. The USPS is having a contest to win a romantic $10,000 trip if able to guess how many Hershey's Kisses does it takes to fill a Priority Mail Flat Rate Box (11 7/8 X 3 3/8 X 13 5/8).

The contest picture had the flat rate box and an artist's rendition of silvered foiled kisses in 'perspective'. The kisses were of different sizes could be a clue. Miniature kisses are about half the size or the original version and both have silver foil. I thought to myself, that's how "they gotcha" because two different sizes are to be used. But wait, this is supposed to be for Valentine's day, wouldn't the box be filled with the special Cherry Cordial kisses made for Valentines? Maybe they are just ever so slightly bigger in order to contain the cherry.

I went to the Hershey's website and found numerous kinds of kisses, Dulce de Leche, Mint, Almond Special Dark, Peanut Butter, Coconut and Mini KISS Cookies with Confetti. All appeared to be the around the same size except for the Giant Hershey Kiss which is filled with kisses. The thirty dollar kiss is so big that it's too wide to fit inside the flat rate box.

The contest operators are not going to just give away $10,000 on an answer that a high school student can figure out the volume using a geometry cone equation. Or a person who simply buys a bunch of Hershey's Kisses, fills a box, and then count afterwards. The contest says anyone who is closest - without going over. One kind of estimate is the volume of the box divided by the volume of a standard kiss, assuming a neatly stacked filled box.