Question

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

Answer 1

Radius of hemisphere $=4.2cm$

Height of toy $=10.2cm$

$\Rightarrow$ Height of the cone $=10.2-4.2=6cm$

And the radius of the cone $=4.2cm$

The volume of the toy $=$ Volume of the hemisphere $+$ Volume of the cone

Volume of the toy $=\frac{2}{3}\pi r^3+\frac{1}{3}\pi r^{2}h$

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

$=\frac{1}{3}\times \frac{22}{7}\times {\left(4.2\right)}^2\times (2\times 4.2+6)$

$=266.112{cm}^3$