Question

The volume of a right circular cone is $1232{cm}^3$ and its height is $24cm$. Find the slant height of the cone.

Answer 1

Given, height of cone $\left(h\right)=24cm$
Let radius of the cone be r.
Volume of the cone $=1232{cm}^3$
$\begin{array}{c}\therefore \frac{1}{3}\pi r^{2}h=1232\\ \Rightarrow \frac{1}{3}\times \frac{22}{7}\times r^2\times 24=1232\\ \begin{array}{cc}\Rightarrow r^2& =\frac{1232\times 3\times 7}{22\times 24}\\ & =49\\ r& =\sqrt{49}\\ & =\sqrt{7\times 7}\\ r& =7cm\end{array}\end{array}$
$\therefore$ radius of the cone $=7cm$
$\because$ slant height of cone (l)$=\sqrt{h^2+r^2}$
$=\sqrt{(24{)}^2+(7{)}^2}$
$=\sqrt{576+49}$
$=\sqrt{625}$
$=\sqrt{25\times 25}$
$l=25cm$
Hence, the slant height of the cone $=25cm$.