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

**Answer:**

1 |

3 |

^{3}

**Step by Step Explanation:**

- 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 - We know,

Volume of the cone =

πr1 3 ^{2}h - Therefore, the volume of the cone that can be carved out of the solid hemisphere of radius r =

πr1 3 ^{2}× r =

πr1 3 ^{3}