## How big is your pizza?

I had lunch at Frankie & Benny’s in Westwood Cross yesterday and chose a 10” American Hot pizza. The pizza was delicious, I can recommend it, and at £9.95 it’s not bad value, but I couldn’t help noticing that the guy at the next table had a 15” pizza and couldn’t finish it, so they boxed up the remains for him to take home. At £13.95 I’d say the 15” is pretty good value too, but only if you can finish it. If you end up throwing half of it away, maybe it’s not such good value. Or is it? Just how much bigger is a 15” diameter pizza than a 10”? It’s not actually a difficult question, I worked it out for myself in a matter of moments over lunch. No doubt you can work it out too, it’s primary school maths, so why not go ahead and have a try.

Done it?

Okay, hands up if you worked out that the 15” pizza is half as big again as the 10”. You’d be wrong, of course. The size of the pizza, given that it’s round (the clue was in the use of ‘diameter’ in the previous paragraph) is represented by its area, and can be calculated using the trusty old formula you probably learned in primary school:

area = π x r^{2}

where r is the radius and is half the diameter, and π is a constant (approximately 3.14 and a bit). Because the 10” pizza has a diameter of 10, the radius is 5, so:

Area of 10” pizza = π x 5^{2} = just over 78.5 square inches.

Pretty impressive for only £9.95, and works out at around 12.7p per square inch. The 15” pizza will be larger than that, obviously, but by how much? Half as much again? Double the size? Less than double? More? What do you think? The radius of the 15” pizza is 7.5, so:

Area of 15” pizza = π x 7.5^{2} = just over 176.7 square inches.

Compare the two and we find that the 15” pizza is equivalent to 2.25 (two and a quarter) 10” pizzas, all for just £13.95, around 7.9p per square inch, which I think is great value — if you can eat it. But if you make the mistake of thinking it’s only half as big again, you could be biting off a lot more than you can chew.

As an aside, I once memorised the value of π to about 25 decimal places, simply because, well, why not. It’s not hard to do (though I’ve forgotten it now), but there are people who have memorised π to thousands of decimal places. Why? Well, why not, but I read somewhere that you only need π to 39 decimal digits to measure the circumference of the observable universe (which, let’s face it, is very, very big) to the width of a hydrogen atom (which let’s face it, is very, very small), so for most practical purposes that’s about all you’ll ever need. So here they are:

3.141592653589793238462643383279502884197

Of course, if you know your maths you’ll know that you don’t really need π to determine the relative sizes of the 10” and 15” pizzas. If you take the 5^{2} and 7.5^{2}, that gives 25 and 56.25, which again gives a relative size for the larger of 2.25 times the smaller.

Now, would you like fries with that?

Sunday, 13. July 2014 10:19

Mmm, pizza.

As a test of memory, I learnt pi to thirty decimal places over a couple of days with a friend while at school…

I can still recite it now, but writing it is more difficult; it’s just easier to roll it off the tongue.