Loaf of Bread

In baking a hemispherical loaf of bread of 10 inch radius, the crust was everywhere of an equal thickness, and the solidity of the crust was equal to half the solid content of the whole loaf. What were the dimensions of the interior soft part?

The Mathematical Correspondent, Volume 1, 1804

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The answer is: the interior soft part is the upper portion of a sphere with radius \(5\sqrt{3} \approx 8.660\) inches, where the portion has height \(10(\sqrt{3}-1) \approx 7.321\) inches and width \(20\sqrt{\sqrt{3}-1}\approx 17.112\) inches at the base

"Loaf of Bread," Convergence (March 2006)

Convergence