Question

Find the capacity in liters 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 cone, r = 7cm
Slant height of the cone, l = 25cm
Height of the cone, $h = \sqrt{l² - r²}$
$= \sqrt{(25)² - (7)²}$
$= \sqrt{625 \- 49}$
$= \sqrt{576}$
h = 24 cm

Volume of cone =$\frac{1}{3}$ $\pi$r²h
= $\frac{1}{3}$ × $\frac{22}{7}$ × 7 cm × 7 cm × 24 cm
= 1232 cm³
= 1232 × ($\frac{1}{1000}$L)
= 1.232 liters

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(ii) Height of the cone, h = 7cm
Slant height of the cone, l = 13cm
Radius of the cone, $r = \sqrt{l² - h²}$
$= \sqrt{(13)² - (12)²}$
$= \sqrt{169 -144}$
$= \sqrt{25}$
r = 5 cm

Volume of the cone = \frac{1}{3}$$\pir²h
= $\frac{1}{3}$ × $\frac{22}{7}$ × 5 cm × 5 cm × 12 cm
$= \frac{2200}{7}$ cm³
$= \frac{2200}{7} × \frac{1}{1000}\ L$
$=\frac{ 11}{35}$ litres