Question

If the radius and height of a cone are in the ratio $5:12$ and its volume is $314c{m}^3$, then its slant height is:

• A. $12cm$
• B. $10cm$
• C. $13cm$
• D. $15cm$

Answer 1

The correct option is C $13cm$

The ratio of the radius and height of a cone is $5:12$.
$\frac{r}{h}=\frac{5}{12}$. ...... (1)
The volume of the cone $=314c{m}^3$
$⟹$ $\frac{1}{3}\pi r^{2}h=314$
$⟹$ $r^{2}h=300$. ........ (2)
On solving equation (1) and (2), we get,
$r=5cm$ and $h=12cm$.
Then, the slant height is $l=\sqrt{h^2+r^2}$
$⟹$ $l=\sqrt{{12}^2+5^2}$
$⟹$ $l=13cm$.
Hence, option $C$ is correct.