Question

The radius and height of a right circular cone are in the ratio of $5:12$. If its volume is $314{cm}^3$ its slant height is:

• A. $26cm$
• B. $19.5cm$
• C. $13cm$
• D. none

Answer 1

Answer: (C)

$13cm$

Given, the ratio of radius and height of circular cone $=5:12$.

Let the radius and height of the cone be $5k$ and $12k$, respectively.

Also, given volume of cone $=314c{m}^3$.

We know, volume of cone $V=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times 3.14\times {\left(5k\right)}^2\times 12k=314$

$\Rightarrow 3.14\times 25\times 4k^3=314$

$\Rightarrow 3.14\times 100k^3=314$

$\Rightarrow 314k^3=314$

$\Rightarrow k=1$.

$\therefore r=5$cm and $h=12$cm.

Slant height $l=\sqrt{r^2+h^2}$

$=\sqrt{5^2+{12}^2}$

$=\sqrt{25+144}$

$=\sqrt{169}$

$=13$ cm.

Hence, the slant height of the cone are $13$cm

Therefore, option $C$ is correct.