Question

Find the capacity in liters of a conical vessel with radius $7cm$ and slant height $25cm$.

Answer 1

Given, radius of the vessel,$r=7cm$

Slant height of the vessel, $l=25cm$

$\therefore$ height of the vessel, $h=\sqrt{l^2-r^2}$

$=\sqrt{{25}^2-7^2}cm$

$=\sqrt{625-49}cm$

$=\sqrt{576}cm$

$=24cm$

Volume of conical vessel

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

$=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 24c{m}^3$

$=1232c{m}^3$

Now, we know, $1000l=1m^3$

$1m^3={10}^{6}c{m}^3$

$1c{m}^3={10}^{-6}{m}^3$

$\therefore 1232c{m}^3=1232\times {10}^{-6}{m}^3$

$\therefore 1232c{m}^3=1000\times {10}^{-6}\times 1232liters$

$\therefore 1232c{m}^3={10}^{-3}\times 1232liters$

$\therefore 1232c{m}^3=1.232liters.$

Hence, the capacity is $1.232liters$