Question

A toy is in the shape of cone mounted on hemisphere of same base radius. If the volume of the toy is $231{cm}^3$ and its diameter is $7cm$, find the height of the toy.

Answer 1

Diameter of the toy $=7cm$

Radius of the toy $=\frac{7}{2}cm=3.5cm$

Volume of the toy $=231c{m}^3$ [Given]

Toy is made of cone and hemisphere of the same base radius.

Volume of the toy = Volume of the cone + Volume of the hemisphere

$\Rightarrow 231=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^3$

$\Rightarrow 231=\frac{1}{3}\pi r^2[h+2r]$

$\Rightarrow 231=\frac{1}{3}\times \frac{22}{7}\times (\frac{7}{2}{)}^2\times [h+2\times 3.5]$

$\Rightarrow 231=\frac{1}{3}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times [h+7]$

$\Rightarrow \frac{231\times 3\times 2}{11\times 7}=h+7$

$\Rightarrow h=11cm$

height of the toy $=h+r=11+3.5=14.5cm$

Hence, height of the toy is $14.5cm.$