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  • A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of pi.

1. A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of \pi.

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The volume of the solid is given by :

The volume of solid  =   Volume of cone   +   Volume of a hemisphere

The volume of cone    :

                                         =\ \frac{1}{3} \pi r^2h

or                                     =\ \frac{1}{3} \pi \times 1^2\times 1

or                                     =\ \frac{\pi}{3}\ cm^3

And the volume of the hemisphere :

                                            =\ \frac{2}{3}\pi r^3

or                                        =\ \frac{2}{3}\pi \times 1^3

or                                        =\ \frac{2\pi}{3}\ cm^3

Hence the volume of solid is   :        

                                           =\ \frac{\pi}{3}\ +\ \frac{2\pi}{3}\ =\ \pi\ cm^3

Posted by

Devendra Khairwa

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