Question

Find the capacity in litres of a conical vessel with height $12cm$, slant height $13cm$.

• A. $\frac{11}{35}$litres
• B. $\frac{21}{35}$litres
• C. $\frac{11}{33}$litres
• D. $\frac{12}{35}$litres

Answer 1

The correct option is A $\frac{11}{35}$litres

Given, slant height of conical vessel $l=13cm$
and height of conical vessel $h=12cm$.

Let the radius of vessel$=r$ $cm$.

Then, $r=\sqrt{l^2-h^2}=\sqrt{{\left(13\right)}^2-{\left(12\right)}^2}=\sqrt{169-144}=\sqrt{25}=5cm$.

Now, capacity of vessel/volume of cone $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times \frac{22}{7}\times 5\times 5\times 12$ $=\frac{2200}{7}{cm}^3$.

We know, $1000{cm}^3=1$ litres.
$\therefore$ $\frac{2200}{7}{cm}^3=\frac{2200}{7\times 1000}=\frac{11}{35}$ litres.

Hence, option $A$ is correct.