Find the capacity in litres of a conical vessel with
Question.

Find the capacity in litres of a conical vessel with

(i) radius 7 cm, slant height 25 cm

(ii) height 12 cm, slant height 13 cm

$\left[\right.$ Assume $\left.\pi=\frac{22}{7}\right]$


Solution:

(i) Radius (r) of cone = 7 cm

Slant height (l) of cone = 25 cm

Height $(h)$ of cone $=\sqrt{l^{2}-r^{2}}$

$=\left(\sqrt{25^{2}-7^{2}}\right) \mathrm{cm}$

$=24 \mathrm{~cm}$

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

$=\left(\frac{1}{3} \times \frac{22}{7} \times(7)^{2} \times 24\right) \mathrm{cm}^{3}$

$=(154 \times 8) \mathrm{cm}^{3}$

$=1232 \mathrm{~cm}^{3}$

Therefore, capacity of the conical vessel

$=\left(\frac{1232}{1000}\right)$ litres $\left(1\right.$ litre $\left.=1000 \mathrm{~cm}^{3}\right)$

$=1.232$ litres

(ii) Height (h) of cone = 12 cm

Slant height (l) of cone = 13 cm

Radius $(r)$ of cone $=\sqrt{l^{2}-h^{2}}$

$=\left(\sqrt{13^{2}-12^{2}}\right) \mathrm{cm}$

$=5 \mathrm{~cm}$

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

$=\left[\frac{1}{3} \times \frac{22}{7} \times(5)^{2} \times 12\right] \mathrm{cm}^{3}$

$=\left(4 \times \frac{22}{7} \times 25\right) \mathrm{cm}^{3}$

$=\left(\frac{2200}{7}\right) \mathrm{cm}^{3}$

Therefore, capacity of the conical vessel

$=\left(\frac{2200}{7000}\right)$ litres $\left(1\right.$ litre $\left.=1000 \mathrm{~cm}^{3}\right)$

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