Tuesday, April 10, 2012

Did You Know?

Did you know that you pretty much always want to go with the extra-large pizza, even if there's a special small- or medium-sized pizzas?

Why? Because the extra-large pizza provides deceptively disproportionate value.

You see, pizza is typically (and deceptively) sold by diameter. Choices of small, medium, large and extra-large might include 10-inch, 12-inch, 14-inch and 16-inch options, respectively.

Comparing the diameters, the medium is 20% larger than the small, the large is 17% larger than the medium and the extra-large is 14% larger than the large. The prices are often commensurate with the difference in diameter. For example the prices for small, medium, large and extra-large might be $10, $12, $14 and $16, respectively.

Thing is, the value of the pizza is in how much pizza you actually get to eat. This is defined by the pizza's volume, not its diameter.

Assuming that the pizzas all come with the same crusts and are equally deep (or thick) we can compare the area of each pizza (i.e., the number of square inches covered by each pizza) as a proxy for its volume. To do this we go way back to basic geometry: Π r2, PI times the radius squared. Since PI is involved in all the computations, we can drop it when performing the comparison. That leaves us with just the radius squared.

In fact, for comparison purposes we can just use the diameter squared; we don't need to divide it by to to get the radius.

Comparing the squared values of the diameters (16"x16", 14"x14", 12"x12" and 10"x10") tells a completely different story. For example, although the diameter of the large pizza is 40% greater than that of the small pizza, you get 78% more pizza with the large than the small, almost twice as much.

Although the diameter of the extra-large pizza is 60% greater than the small pizza, you get 156% more pizza with the extra-large than the small. That's 2.56 times as much pizza!

Here are some other comparisons:

I thought you might like to know that.

Happy Tuesday,

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