Can YOU figure out which one is bigger – A 20-inch pizza or two 10-inch pizzas?
- How does the area of two 10 inch pizzas compare with that of one 20 inch pizza?
How do two pizzas with a diameter of 10 inches compare in size to one with a diameter of 20 inches?
If the 20-inch pizza was twice the price of a 10-inch pizza, would you be better off spending your money on two small pizzas or one large one?
Solution:
Assuming the pizzas are perfectly circular disks and have the same uniform height, their volume can be calculated as follows:
The area of a circle is the radius (half the diameter) squared, multiplied by pi (3.14…).
The smaller 10-inch pie therefore has an area of:
5 inches x 5 inches x ~3.14 = 78.5 square inches
Two 10-inch pizzas therefore have a total area of around 157 square inches
The larger 20-inch pie has an area of:
10 inches x 10 inches x ~3.14 = 314 square inches
Since 10 squared is 4 times larger than 5 squared, the area of the larger pizza is four times that of the smaller one.
The 20-inch pizza is therefore twice the size of the two 10-inch pizzas.
This can be visualized in a graphic that shows two smaller pizzas placed next to each other and on top of the larger one:
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