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Why You Should Always Order the Large Pizza

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I am a former maths teacher and owner of Doingmaths. I love writing about maths, its applications and fun mathematical facts.

What Should You Order? One Large Pizza Or Two Medium Pizzas?

We all know the predicament. You're looking through the menu for the pizza takeaway and notice they have a special offer on for medium pizzas. You can get two medium 12-inch pizzas for the same price as one large 18-inch pizza. It seems like a no-brainer. Surely the two medium pizzas will give you more pizza, hence a better deal. Or do they?

Let's take a look at the maths.

Mathematics Finds the Best Deal

Fortunately, it's fairly simple to work out how much pizza we would be getting for each option. The pizzas are circles and the formula for the area of a circle is area = π × (radius)2. Our pizzas' measurements are for the diameters, so by halving these and substituting them into the formula, we can find the areas of our pizzas.

  • Area of one large 18-inch pizza = π × 92 = 254.5 in2
  • Area of two medium 12-inch pizzas = 2 × π × 62 = 226.2 in2

So there we have it. You get more pizza from one large 18-inch pizza than you do for two medium 12-inch pizzas.

What About the Crusts?

There is another issue to be explored, however: what about the crusts?

Some people love the crusts (especially if they are stuffed crusts), whereas some people don't like them at all. As this can also affect which choice is the best, we're going to look at this too.

For ease of calculation, let's assume that the crust is 1-inch wide. We can calculate the area of crust for each option by working out how much non-crust pizza there is and subtracting this from our earlier pizza area answers. As the crust is 1-inch wide, the radius of the non-crust part of the pizza must be 1 inch less than that of the whole pizza (8 inches for the large pizza and 5 inches for the medium pizzas).

  • Area of crust on large pizza = 254.5 - π × 82 = 53.4 in2
  • Area of crust on two medium pizzas = 226.2 - 2 × π × 52 = 69.1 in2

So the medium pizzas provide slightly more crust, which may sway the choice for any stuffed crust lovers out there.

'Which Size Pizza Should You Order?' on the DoingMaths YouTube channel

Conclusion

So the maths has decided it. If you are looking for the most pizza for your money, you should go with one large pizza.

If you are a crust-fiend and want that extra bit of crust on your pizza, then you should go with the two medium pizzas.

© 2020 David

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