The sum of a surface area of a sphere and a cube is given. Show that when the sum of their volumes is least, the diameter of the sphere is equal to the edge of a cube.

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The sum of a surface area of a sphere and a cube is given. Show that when the sum of their volumes is least, the diameter of the sphere is equal to the edge of a cube.

The surface area of a sphere is given by `SA=4pir^2`
The surface area of a cube is given by    `SA=6s^2`
where r is the radius of the sphere and s is the side length of the cube.

Let the sum of surface areas be k, so `k=4pir^2+6s^2` . Then we can solve for s

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