Multiple choice

The sum of the surface areas of a sphere and a cube is given. When sum of their volumes is least, the ratio of the radius of the sphere and the edge of the cube is

  1. 1 : 2

  2. 2 : 1

  3. 2 : 3

  4. 3 : 2
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A Correct answer
Explanation

Let r be the radius of the sphere and x be the edge of the cube. Surface area S = 4*pi*r^2 + 6*x^2. Volume V = (4/3)*pi*r^3 + x^3. Minimizing V subject to constant S leads to the condition where the derivative of V with respect to r (using x as a function of r) is zero, resulting in r = x/2, or r:x = 1:2.

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