Question

# A toy is in the form of a cone of radius $rcm$ mounted on a hemisphere of same radius. The total height of the toy is $\left(r+h\right)cm$, then the volume of the toy is?

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Solution

## Given that,The radius of the toy is $rcm$ and mounted on a hemisphere of the same radius.Since, The total height of the toy is $\left(r+h\right)cm$, so the height of the cone is $hcm$Now, The volume of the toy $=$ Volume of cone $+$ Volume of the hemisphere So, Volume of the toy $=\frac{1}{3}{\mathrm{\pi r}}^{2}\mathrm{h}+\frac{2}{3}{\mathrm{\pi r}}^{3}$ $=\frac{1}{3}{\mathrm{\pi r}}^{2}\left(\mathrm{h}+2\mathrm{r}\right)$Hence the volume of the toy is $\frac{1}{3}{\mathrm{\pi r}}^{2}\left(\mathrm{h}+2\mathrm{r}\right)$.

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