Scaling a pizza from six diners to eight

Question

A pizza with a 12-inch diameter feeds six people. What diameter is needed to feed eight people with the same portion each?

Short answer

About $13.9$ inches. Servings scale with area, which is proportional to diameter squared, so $d = 12\sqrt{8/6} = 12\sqrt{4/3} \approx 13.86$ . A one-third increase in area needs only about a $15\%$ increase in diameter.

Adapted from Crack, Heard on the Street, Q2.44, p.30; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

The Black-Scholes PDE, Formula and Implied Volatility
Derivation — From Binomial Trees to Black-Scholes in the Continuous Limit
The Black-Scholes Formula Derived via Change of Measure

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