Two small pizzas instead of one? Think twice!

Why you should always order the large pizza?

We often see these deals, buy 2 for 1! Is this real thing? Maybe for some products, but for sure this will not work for pizza! Nota-a-chance!

So let's take a closer look 👀

You need to choose between ordering two small size pizzas, each with radius 10 cm, while on the other side the large pizza, which has a larger radius of 20 cm.

We can approach this problem in two ways: arithmetically or maybe we can say visually.

The arithmetic method would require from us to calculate the area for each pf the pizzas. Since we are here, let's do that. 

Let's denote the area of the small pizza by Pr, 

and the area of the large pizza by PR. 

Then we have:

Pr=p10^2, and PR=p20^2, which equals to

Pr=100p, and PR=400p.

Can you notice the ratio? Yup! Two small pizzas are altogether 200p, and the large one is 400p.

The conclusion if you want to eat more (not always necessary and healthy choice) you should buy the large one! Don't let be tricked.

This type of problem is often seen as well as the following (borrowed from Mathematical Curiosities, by A. Posamaniter and I. Lehmann, p 172):

"Would a bathtub drain quickly with a single drain hole of diameter two inches, as with two drain holes of diameter one inch?"

In the same book the authors present another "surprisingly simple-yet often -overlooked" solution, when they say: "We can also make the comparison geometrically by merely inspecting the cross-sections superimposed over one another". Basically, what they want to say is that , if you draw the larger circle, then lay the two circles inside of it, so that circle have only one common point, then it's OBVIOUS what is going on.