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  • The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.

Direction: Write True or False and justify your answer in each of the following :

The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.

 

Answers (1)

Answer: True

We know that

Volume of cone =\frac{1}{3}\pi r^{2}h   (where r is the radius and h is height)

Volume of the hemisphere =\frac{2}{3}\pi r^{3}    (where r is the radius)

For largest right circular cone that can be fitted in a cube whose edge is 2r, the height of cone will be 2r and its diameter will also be equal to 2r. So, radius of its base is equal to r.

So, volume of cone =\frac{1}{3}\pi r^{2}\left ( 2r \right )=\frac{2}{3}\pi r^{3}

                                = volume of hemisphere

Thus, the statement is true.

Posted by

infoexpert23

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