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What is the proportion between the height of the cone with the largest possible volume that can fit inside a sphere and the sphere's diameter?

1. 2/3
2. 3/4
3. 1/3
4. 1/4

Correct answer: 2/3

Solution

To maximize the volume of a cone that fits inside a sphere, the height of the cone should be 2/3 of the diameter of the sphere, because the volume of the cone is proportional to the cube of its height, and the height of the cone is limited by the diameter of the sphere

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