The inside of a bowl is part of a sphere. When water is put into the bowl to a depth d, the water surface becomes a circle of radius 2d. What is the radius of the sphere?

Explanation

Using the Pythagorean theorem on the cross-section of the sphere: R^2 = (R-d)^2 + r^2. Substituting r = 2d yields R^2 = R^2 - 2Rd + d^2 + 4d^2 \implies 2Rd = 5d^2 \implies R = 2.5d.

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