# Sizing Science: The Geometry of M&Ms

A candy challenge from Science Buddies

Observations and results
Did you find the ellipsoid formula to give the closest answer to the actual volume you measured for one M&M candy?

Using the water displacement test, you should have found the actual volume of a single M&M candy to be about 0.60 to 0.65 cubic centimeter (milliliter). (Adding 100 M&Ms to 100 ml of water should have caused the water level to rise to about 160 to 165 ml.) When using the sphere formula with the long radius, the calculation gives a volume (about 1.3 cubic centimeters) that is a little bigger than the actual volume of the M&M candy. If you look closely, you will see that the volume of an M&M is not quite perfectly round but is shaped like a sphere that has been squished on one side. If it were not "squished," the sphere formula with the long radius would fit. The cylinder formula also gives a volume (about one cubic centimeter) that is too big because it assumes that the entire length of the M&M is as wide as its short diameter is, but it actually tapers around the edges. The sphere formula with the short radius gives a volume (about 0.2 cubic centimeter) that is much smaller than the actual volume of the M&M. The ellipsoid formula should give a volume (about 0.6 cubic centimeter) that is very close to the actual volume of the candy. An M&M indeed has an ellipsoid shape, specifically, a type called an oblate spheroid.

Cleanup
•     If portions of the clay or Play-Doh have been dyed by the M&Ms' coating, you can try to pinch these parts out and throw them in the trash.
•     If you want to eat the soggy M&Ms when you are done with this activity, you may do so, but you should not eat the M&Ms that were in contact with the clay or Play-Doh.

More to explore
Agricultural and Biological Engineering: Tools: Unit-Free Volume Calculators from Mississippi State University
Unique Shape of M&M's Interests Scientists from NPR's Talk of the Nation's Science Friday
Math Tables: Areas, Volumes, Surface Areas from Math2.org
Geometry from MathIsFun.com
M&M Geometry from Science Buddies

This activity brought to you in partnership with Science Buddies

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1. 1. tsizemore1982 08:42 PM 11/30/12

Thanks, now my mouth is salivating for some chocolate M&Ms; and my hand is aching for some geometry. LOL. =)

2. 2. Kombarde 09:59 PM 1/1/13

What's about finding a Math formula which will precisely describe M&M model?

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