The Great Takeaway Pizza Con

This is a fun little article to demonstrate how knowledge of a bit of simple mathematics can save you hundreds over your life-time...and make you feel really smug in the process.

The Con

We're all being conned and the worst thing is that most of us don't even realise it. Of course, I'm talking about the great takeaway pizza con. Takeaway pizza companies have been conning us for decades and I want to put a stop to it.
The con is a simple one, based on simple business statistics. Basic psychology teaches us that people prefer a large pizza (12") and not finishing it, to ordering a small (9") pizza and still feeling hungry. Takeaway pizza companies feed off this knowledge and bump up the price of a large. Fair enough, on might say. This is simple supply and demand. However, there is a way to beat the system with knowledge of a little basic mathematics.

The Solution

All you need to know is one simple equation:
The area of a circle A=πr^2,   where r^2 = r * r ,   or r times r, where r is the radius of the circle.
If this seems a little complicated please don't worry, I will guide you with a friendly hand through this mirky mire of mathematics.
Pizza companies usually give you the diameter and price of each pizza size.
For our purposes a small pizza will have a diameter of 9 inches (9") and will cost £2. A large pizza will have a diameter of 12 inches (12") and will cost £5. As you can see the large pizza is more than the cost of two smaller pizzas, but is it worth paying more for the larger pizza? That is, do you get more bang for your buck, or I should say more pizza for your dollar!

The mathematics - don't panic

To work out the radius (r) of a pizza you observe the diameter and halve it. Whilst we know that π is a really long number that starts 3.141592654.....all we need to do is work out our answers in terms of π.

In the case of the small pizza: the area of the pizza = πr^2. Since the diameter of this pizza is 9" thus the radius is 4.5" (half of the diameter). This means that the area of the pizza = π(4.5)*(4.5).
Using my brilliant calculator like mind we can see that this is = 20.25π which cost you £2.
Thus if you bought two 9" pizzas you could get 40.5π worth of pizza for £4.

In the case of the large pizza: Since the diameter of this pizza is 12" thus the radius is 6" (half the diameter). This means that the area of the pizza = π(6)*(6)
The area of the pizza = 36π which cost you £5.

It doesn't take a genius now to see that if you had bought two small pizzas you would get more pizza for 20% off the cost of a large pizza.

Doesn't it make sense to always buy two smaller pizzas saving you a little cash and giving you more food!

The conclusions

This sort of thing doesn't just happen in pizzas, it happens in all sorts of goods in the supermarket as well. Buying in bulk is not always so beneficial. Always check the £ per kilogram if the have it (or equivalent metric and currency).

Hope you enjoyed this brief mathematical thought experiment and that it wasn't too tough for any of you. Please let me know what you thought of my findings in the comments section below.

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1 comment

Get Rich Point said...

Good analysis. Next time I am going to order two pizzas instead of one big pizza.

I didn't misunderstand your post the first time either but I do admit the mistake of not rechecking my comment.

Sorry! Please don't harbor the sour feeling that I read your post uninterested.I am an engineer and there is no reason why I wouldn't understand it. However, it seems that my vanity never permits me to recheck things I leave behind.This mistake will never be repeated.Thanks for teaching me a lesson.