### Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r. A B O r r V

 1 3
πr3

Step by Step Explanation:
1. Clearly, the radius of the base of the cone will be equal to the radius of the hemisphere.
So, radius of the base of the cone = r

Also, the height of the cone equals to the radius of the hemisphere.
So, height of the cone = r
2. We know,
Volume of the cone =
 1 3
πr2 h
3. Therefore, the volume of the cone that can be carved out of the solid hemisphere of radius r =
 1 3
πr2 × r =
 1 3
πr3

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