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 $(r+h)cm$, then the volume of the toy is?

Answer 1

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 $(r+h)cm$, 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 $=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}+\frac{2}{3}{\mathrm{\pi r}}^3$

$=\frac{1}{3}{\mathrm{\pi r}}^2(\mathrm{h}+2\mathrm{r})$

Hence the volume of the toy is $\frac{1}{3}{\mathrm{\pi r}}^2(\mathrm{h}+2\mathrm{r})$.