Question

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

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Solution

## $r=1cm$$h=1cm$We have to find out the volume of the solid in terms of $\mathrm{\pi }$Total Volume$=$ Volume of cone $+$ Volume of HemisphereWe know that:Volume of cone$\mathbf{=}\frac{\mathbf{1}}{\mathbf{3}}\mathbit{\pi }{\mathbit{r}}^{\mathbf{2}}\mathbf{h}$Volume of hemisphere $=\frac{2}{3}{\mathrm{\pi r}}^{3}$$=\frac{1}{3}{\mathrm{\pi r}}^{2}\mathrm{h}+\frac{2}{3}{\mathrm{\pi r}}^{3}\phantom{\rule{0ex}{0ex}}=\frac{1}{3}{\mathrm{\pi r}}^{2}\left(\mathrm{h}+2\mathrm{r}\right)\phantom{\rule{0ex}{0ex}}=\frac{1}{3}×\mathrm{\pi }×1×1×\left(1+2\right)\phantom{\rule{0ex}{0ex}}=\mathrm{\pi }{\mathrm{cm}}^{3}$Hence, the volume of the solid is $\mathrm{\pi }{\mathrm{cm}}^{3}$.

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