Question

Find the capacity in litres of a conical vessel with
(i) radius $7cm$, slant height $25cm$.
(ii) height $12cm$, slant height $13cm$.

Answer 1

Given:

(i) $r=7$, $h=25$cm

$\Rightarrow$$h=\sqrt{l^2-r^2}$

$\Rightarrow$$\sqrt{{25}^2-7^2}=\sqrt{576}$

$\Rightarrow$$h=24$

$\Rightarrow$$V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 7\times 24$

$\Rightarrow$$154\times 8=1232$cm${}^3$

$\Rightarrow$$1.232$ litres

(ii) $h=12$cm, $l=13cm$

$\Rightarrow$$r=\sqrt{l^2-h^2}$

$\Rightarrow$$\sqrt{{13}^2-{12}^2}=\sqrt{25}=5$

$\Rightarrow$Volume $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 5\times 5\times 12$

$\Rightarrow$$\frac{2200}{7}$cm${}^3=\frac{2200}{7\times 1000}$ litres

$\Rightarrow$$\frac{11}{35}$ litres