How many Hershey's Kisses, do you think fit in a USPS Flat Rate Priority Mail box?

Question

( here are the Box dimensions: 11 7/8" x 3 3/8" x 13 5/8." )

Answer 1

This is a typical Fermi problem. but the solution is fairly simple

First estimate the size of a "Hershy kiss" about 1" diameter. about 1" high: giving a volume of 1/3 PI d^2 h /4 or about 0.26 cubic inches.

Next estimate the volume of the mailing box: about 543.8 cubic inches

if you would divide the volume of the box by the volume of a "kiss" (approximately 2635) you would get an over-estimate of the number of "kisses"
That is because the kisses have round bases. For objects like Hershey kisses the packing ratio is only about 60 % so the number of kisses is only about 60% of 2635 or about 1581.

You could pack a little less than 1600 Hershey kisses in that USPS box.

P.S. donryan00 is quite corect, the volume of the box is 546.06..... cubic inches, but that is only 0.42% higher than my original value, thus the result will increase by 0.42% of 1581 or about 7 "kisses" to 1588 and the final concluion of "a little less than 1600 Kisses" is still correct.
Thanx for the correction Donryan00

Answer 2

I believe it is more around 1500, than 1600, after doing some extensive mathematical analysis.

I believe kisses are more like 13/16 of an inch in diameter and height. This fits with the 1.65 cubic centimeters pure chocolate (add wrapper and get 0.14 cubic inches).

Also, 60% of box volume doesn't appear right from my complex calculations. I am getting more around 40% box volume.

In the end, I get about 1510 for a guess.

My math might not be clear, as I do a bunch of formula variables as adding to the approximation:


Volume Formulas:

Cylinder = pi * radius2 * height
Cone = (1/3) * pi * radius2 * height

------------------------------

FIXED NUMBERS:

Volume of Hershey’s Kiss Chocolate = 1.65 cubic centimeters(0.1 cubic inches)

Volume of Hershey’s Kiss w/ Wrapper = 0.15 cubic inches approximately


MY THEORY:

Cylinder Area:
+ 1 Primary Hershey’s Kiss Volume: (1/3) * pi * radius_a2 * height_a
+ 10(effective not actual) Secondary Hershey’s Kisses Contrib. Vol.: (1/3) * pi * radius_b2 * height_b

radius_a = 13/32 inches
height_a = 13/16 inches

height_b = ½ radius_a = 13/64 inches
radius_b = 13/128 inches

Volume Ratio = X / Cyl. Vol
X = (1/3) * pi * radius_a2 * height_a + 10 x ((1/3) * pi * radius_b2 * height_b)
X = 0.1404 + 0.0214 = 0.1618

Cyl. Vol w/ Hershey's Kiss radius and height = 0.4213

Volume Ratio = 0.1618 / 0.4213 = 0.36886 = 38.5% of box filled.
My Guess is 40% box filled.

Flat Rate Box Volume = 546 cubic inches (or 515 maybe if 546 is outer measurement)

Estimate at 530 cubic inches

AMOUNT OF KISSES = (530 / 0.1404) x 40% = 1509 kisses


Tony

Answer 3

Usps Hershey

Answer 4

Well, after doing some research and math, I would say about 2502. But this number does not factor in many variables such as empty/wasted space, space for the wrappers & plumes, and the density of chocolate used by Hershey's. If I were to make an educated guess, I'd say the number is perhaps closer to 2400. You could always get a box form your local post office, and several bags of Kisses, but that might be pricey.

Answer 5

Hats off to Simply Wisdom's answer but I don't think it will matter. We won't know how the PO is going to fill the box to get their number. For example they could pour kisses into their reference box and then count it to get one number or they could pour it 3/4 of the way and then shake it to loosen the air pockets and put more in it. There's no clear way to verify their methodology. That's part of the challenge in that it can't be purely calculated since you're missing a few variables.

Answer 6

I disagree with the Fermi solution in that they will settle as they travel. Each will find the most available space. Add to that the fact that you can stretch another 1/2 " in all dimensions of the box.

2952 if my opinion.

Answer 7

Isn't the volume of the box 546.064453125?

There's no way to precisely measure the size of the kiss, is there? A conical volume formula wouldn't be exact, since it isn't an exact cone.

Answer 8

STOP CHEATING AND GUESSTIMATE YOUR OWN ANSWER.

This is a Valentine's Day Contest Sponsored by the US Postal Service and the grand prize is $10,000 to win a Romantic Trip of your dreams. It's unfair to have other people doing the work for you.

Answer 9

707

Answer 10

1342