Question

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

Answer 1

Radius of vessel $\left(r\right)=7cm$

Slant height of vessel $\left(l\right)=25cm$

Height of vessel $\left(h\right)=?$

As we know that,

$l^2=h^2+r^2$

$\Rightarrow h^2={\left(25\right)}^2-{\left(7\right)}^2$

$\Rightarrow h=\sqrt{625-49}=\sqrt{576}=24cm$

Therefore,

Capacity of vessel $=$ Volume of cone

Therefore,

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

$=\frac{1}{3}\times \frac{22}{7}\times 7^2\times 24$

$=22\times 7\times 8$

$=1232{cm}^3$

$=1.232L(\because 1000{cm}^3=1L)$