Biggest Pizza Slice

An 8-inch pizza is cut into 3 equal slices. A 10-inch pizza is cut into 4 equal slices. A 12-inch pizza is cut into 6 equal slices. A 14-inch pizza is cut into 8 equal slices. From which pizza would you take a slice if you want as much pizza as possible?
Source: NCTM Mathematics Teacher, September 2006

Solution
Areas of pizza slices
8-inch: \dfrac{\pi\times 4^2}{3}=\dfrac{\pi\times 16}{3}=\dfrac{\pi\times 128}{24}
10-inch: \dfrac{\pi\times 5^2}{4}=\dfrac{\pi\times 25}{4}=\dfrac{\pi\times 150}{24}
12-inch: \dfrac{\pi\times 6^2}{6}=\dfrac{\pi\times 6^2}{6}=\dfrac{\pi\times 144}{24}
14-inch: \dfrac{\pi\times 7^2}{8}=\dfrac{\pi\times 49}{8}=\dfrac{\pi\times 147}{24}
Since \dfrac{150}{24} is the largest fraction, you want to take a slice from the 10-inch pizza.

Answer: 10-inch pizza

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About mvtrinh

Retired high school math teacher.
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