Question

The height and the slant height of a cone are $21$ cm and $28$ cm, respectively. Find the volume of the cone.

Answer 1

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

Given

Slant height$=l=28cm$

Height of cone $=h=21cm$

Let radius of cone $=r$cm

We know that

$l^2=h^2+r^2$

${28}^2={21}^2+r^2$

$\Rightarrow {28}^2-{21}^2=r^2$

$\Rightarrow r^2=\sqrt{7.49}$

$\Rightarrow r=7\sqrt{7}cm$

So,

Volume of cone $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\cdot \frac{22}{7}\cdot 7\sqrt{7}\cdot 7\sqrt{7}\cdot 21c{m}^3$

$=22\cdot 7\sqrt{7}\cdot 7\sqrt{7}c{m}^3$

$=\mathrm{22.7.7.}(\sqrt{7}{)}^{2}c{m}^3$

$=\mathrm{22.7.7.7}c{m}^3$

$=7546c{m}^3$

$\therefore$ Volume of cone $=7546c{m}^3$.