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


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Answer:

 

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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