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 $\pi$.

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   :

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

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