Q2 of 51 Page 1

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

Given: Radius of hemisphere = r


To find: The volume of the hemisphere.


Formula Used: Volume of cone =


Explanation:



As we know the radius of the base of hemisphere = height of hemisphere = r


Also, in this figure:


radius of cone = radius of hemisphere = r


⇒ Height of cone = radius of hemisphere = r


Using the formula given above,


The volume of the cone =


Here h = r


⇒ The volume of the cone =



Hence, the maximum volume of cone is cubic units.


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