Question

Question 2 (ii)
Find the capacity in litres of a conical vessel with:
(ii) height 12 cm, slant height 12 cm.
$[Assume\pi =\frac{22}{7}]$

Answer 1

(ii) Height (h) of the cone = 12 cm
Slant height (l) of the cone= 13 cm
Radius (r) of cone $=\sqrt{l^2-r^2}$
$=\left(\sqrt{{13}^2-{12}^2}\right)cm$
$=5cm$
Volume of the cone $=\frac{1}{3}\pi r^{2}h$
$=[\frac{1}{3}\times \frac{22}{7}\times (5{)}^2\times 12]c{m}^3$
$=(4\times \frac{22}{7}\times 25)c{m}^3$
$=\left(\frac{2200}{7}\right)c{m}^3$
Therefore, capacity of the conical vessel
$=\frac{2200}{7000}litres(\because 1litre=1000c{m}^3)=\frac{11}{35}litres$