Question

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

Answer 1

Given:

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

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

$r=OA=4.2cm$

$h=VO=V{O}^{\prime }-O{O}^{\prime }=(10.2-4.2)cm=6cm$

Volume of the wooden toy
= Volume of the conical part + Volume of the hemispherical part

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

$=\frac{\pi r^2}{3}(h+2r)c{m}^3$

$=\frac{1}{3}\times \frac{22}{7}\times 4.2\times 4.2\times (6+(2\times 4.2\left)\right)c{m}^3$ [Since $h=10.2-4.2=6cm$]

$=\frac{1}{3}\times \frac{22}{7}\times 4.2\times 4.2\times 14.4c{m}^3=266.11c{m}^3$