PI-zza

Geometry Level 2

Pete's Pizzaria is offering a circular pizza of diameter 18 and a square pizza of side length 16 for the same price.

Which pizza is a better buy? (Ignore the crusts)

Circular Pizza They have the same area Square Pizza

Chung Kevin by Chung Kevin , 45, Australia

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1 solution

Chung Kevin
Jan 30, 2017

I don't know how to approximate this without using a calculator. We can calculate that

π × 9 2 = 254.5 < 256 = 1 6 2 , \pi \times 9^2 = 254.5 < 256 = 16 ^ 2,

so the square pizza is a better buy.

I found out that π ≈ ( 4 3 ) 4 \pi \approx \left( \frac{4}{3} \right)^4 , and I was surprised at how simple these numbers are, which led to this problem.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

We just need to show that π < 22 7 < ( 4 3 ) 4 \pi < \frac{22}7 < \left ( \frac43\right)^4 .

The first part of the inequality has been proven .

Pi Han Goh - 4 years, 4 months ago

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