Larger Pizza or Two Smaller Ones: Which Provides More Pizza?

When deciding between ordering a larger pizza or two smaller ones, you might wonder which option provides more pizza by weight or by surface area. This article explores the mathematical basis for this decision, using straightforward geometric principles to help you choose wisely.

Mathematics of Pizza Area

The area of a pizza or any circle is calculated by the formula pi times the radius squared. Given that pi is approximately 3.14159, it is often simplified in calculations. For a 17-inch pizza, the area is approximately 254.47 square inches, while two 12-inch pizzas combined have an area of about 226.2 square inches. This shows that a single 17-inch pizza offers slightly more area compared to two 12-inch pizzas.

Comparing One 18-inch Pizza to Two 12-inch Pizzas

Let's delve deeper into the numbers. An 18-inch pizza has a radius of 9 inches, giving it an area of 254.47 square inches. On the other hand, two 12-inch pizzas have a combined area of 226.2 square inches. In this comparison, the 18-inch pizza indeed offers more pizza by surface area.

Considering the Crust: Total Food Consumption

The choice also depends on whether you want to include the crust in your calculation. If you exclude the crust, an 18-inch pizza without crust offers 201 square inches, while two 12-inch pizzas with crust yield about 157 square inches. This means that even without the crust, a single 18-inch pizza provides more food than two smaller ones.

Practical Implications

To make sense of the numbers, let's break it down further:

The 18-inch pizza provides more surface area, offering 254.47 square inches. Two 12-inch pizzas combined offer 226.2 square inches. When the crust is considered, the difference is even more significant, with the 18-inch pizza being nearly 44 square inches larger.

Mathematically, there is no doubt. However, different people might have different preferences. Some might prefer smaller, bite-sized pieces, while others prefer a larger, more substantial slice without the crust.

Conclusion

While the 18-inch pizza offers more surface area, whether to choose it over two smaller pizzas depends on personal preference and the amount of crust one is willing to give up. Understanding the math behind it can help you make a more informed decision the next time you're ordering pizza.

References:

Area of a Circle