The volume of a cone of radius 7 cm and slant height 14 cm is ______.(use π=22

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The volume of a cone of radius 7 $c m$ and slant height 14 $c m$ is ______.
$(u s e π = \frac{22}{7})$

Options:

A .

622.381 c m^{3}

B .

722.381 c m^{3}

C .

618.381 c m^{3}

D .

522.381 c m^{3}

Answer: Option A
:
A

Given,
Radius of the cone
$r = 7 c m$
Slant height of the cone
$l = 14 c m$

From the pythagoras theorem
$l^{2} = h^{2}$ + $r^{2}$ ,
height of the cone
$h = \sqrt{14^{2} - 7^{2}}$
$h = \sqrt{147} = 12.1243 c m$

Volume of a Cone
$= \frac{1}{3} \times π \times r^{2} h$
$= \frac{1}{3} \times \frac{22}{7} \times 7^{2} \times 12.1243$
$= 622.381 c m^{3}$

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