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Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r.

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Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r.

(A) 4/3 πr3

(B) 2πr3

(C) 1/3 πr3

(D) 2/3 πr3

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Best answer

The correct option is: (C) 1/3 πr3

Explanation:

To cut out maximum area, radius of the cone = radius of the hemisphere = r

and height of the cone = radius of the hemisphere = r

.'. Volume of the cone = 1/3 πr2h = 1/3  πr3

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