You're at a pizza shop with three friends. The menu shows two sizes: a 20-centimetre pizza for 40 yuan, or a 30-centimetre one for 60 yuan. You the smaller one is a better deal because it costs less. Bad move. You just lost almost half your pizza without it.
The is in how circles work. The number on the menu is the , the distance straight across the pizza. But the of pizza you get depends on the area, not the width. And here's where it gets fun. Area grows much faster than diameter.
To the area of a circle, we use the formula π × r², where r is half the diameter. A 20-cm pizza has a radius of 10 cm, so its area is about 314 square centimetres. A 30-cm pizza has a radius of 15 cm and an area of about 707 square centimetres. That is more than the food.
Now the prices. You pay 40 yuan for 314 cm² of pizza, or 60 yuan for 707 cm². The large one gives you 125 percent more food for only 50 percent more money. The cost per bite drops by a third. The of the large pizza is far better. Two small pizzas still would not one large, yet they cost 80 yuan.
Why does everyone get this wrong? It seems after you do the maths, but our eyes are terrible at judging area. A pizza 50 percent wider does not look that much bigger when you see it on the table. Your brain looks at the diameter and guesses wrong. That guess is never .
Next time you order pizza, remember this. The difference comes from a single fact. Area grows with the square of the diameter. Double the width, and you get four times the pizza. Do not your money on two small ones when one big pizza gives you more food for less.
