Question

A solid uniform toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is $4.2cm$ and the total height of the toy is $10.2cm$, find the volume of the wooden toy.

Answer 1

We have $V{O}^{\prime }=10.2cm,OA=O{O}^{\prime }=4.2cm$

Let $r$ be the radius of the hemisphere and $h$ be the height of the conical part of the toy

Then $r=OA=4.2cm$
$h=VO=V{O}^{\prime }-O{O}^{\prime }=(10.2-4.2)cm=6cm$
Also radius of the base of the cone $=OA=r=4.2cm$

Volume of the wooden toy

volume of the conical part + volume of the hemispherical part

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

$=\frac{1}{3}\times \frac{22}{7}\times 4.2\times 4.2\times (6+4.2){cm}^3$

$=266.11{cm}^3$