I was in a local fast food restaurant, who will be left nameless. Anyway, after getting my Mcdrink I thought it seemed a little small. It was called a "large" after all. So I was thinking it should be at least a 32 ounce or 40 ounce drink. Being something of a connoisseur of these things, I felt this was well off.
It reminded me of a time when I verified to a class the measurement of a supposed 32 ounce cup. It was like an episode of Mythbusters. It turned out to indeed be the as advertised 32 ounce container.
I began my investigation by Googling "volume of cup sizes" which led me to websites that were not even close to helpful. Another approach was necessary. The plastic cups found in convenience stores or fast food restaurants are close to, but not quite, cylinders. They slope somewhat so that the top of the cup is a little wider than the bottom. Mathematically, this could be called a truncated cone or a frustrum. To find the volume we multiply the area of the base by the height. The area of the base can be found by using the average of the radii of the two bases.
Getting as close as I could on the measurements, I found radii of 4.85 cm and 3.15 cm and a height of 16.3 cm. We then have an average radius of 4.0 and a total volume of (Pi)(4)(4)(16.3) = 819.3 cubic centimeters. One cubic centimeters is equal to 0.033814 fluid ounces, so we can multiply to find a volume of 27.7 ounces of fluid.
While I know the term "large" is relative, I was a little mcdisappointed nonetheless.
