Question

Finds 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.

Answer 1

(i) Radius of the conical vessel (r)=7 cm

Slant height (h)=25 cm

$\therefore Verticalheight\left(h\right)=\sqrt{l^2-r^2}=\sqrt{(25{)}^2-(7{)}^2}=\sqrt{625-49}=\sqrt{576}=24cm\therefore Volume=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 24c{m}^3=1232c{m}^{3}Capacityinlitres=\frac{1232\times 1}{1000}l=1.232litres$

(ii) Height (h)=12 cm

Slant height (l)=13 cm

$\therefore Radius=\sqrt{l^2-r^2}=\sqrt{(13{)}^2-(12{)}^2}=\sqrt{169-144}=\sqrt{25}=5cm\therefore Volume=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 5\times 5\times 12c{m}^3=\frac{2200}{7}c{m}^3=314.28c{m}^{3}NowCapacityinlitres=\frac{2200}{7\times 1000}l=\frac{22}{70}l=\frac{22}{70}l=0.314litres$