Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r.
Answer:
πr3
Step by Step Explanation:
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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 =
πr2 h1 3 - Therefore, the volume of the cone that can be carved out of the solid hemisphere of radius r =
πr2 × r =1 3
πr31 3