 # A Sector Of A Circle Of Radius 12 Cm Has An Angle 120 . By Coinciding Its Straight Edges A Cone Is Formed. Find The Volume Of Cone.

Given the radius of the circle 12cm

This becomes the slant height of the cone

The angle of sector $$120^{\circ}$$

The length of arc is given as = $$\frac{x}{360} * 2 \Pi r$$ $$\Rightarrow \frac{120}{360} * 2 * \Pi * 12$$ $$\Rightarrow \frac{1}{3}2\Pi * 12$$ $$\Rightarrow 2\Pi * 4$$ $$\Rightarrow 8\Pi$$

This become the circumference of base circle = $$2 \Pi r = 8\Pi$$

2r = 8

r = 4

According to Pythagoras theorem

$$(Slantheight)^{2} = (height)^{2} + (radius)^{2}$$ $$\Rightarrow 12^{2} = (height)^{2} + (4)^{2}$$ $$\Rightarrow 144 = (height)^{2} + 16$$ $$\Rightarrow (height)^{2} = 144 – 16$$ $$\Rightarrow (height)^{2} = 132$$ $$\Rightarrow height = \sqrt{132}$$

The volume of cone =$$\frac{1}{3}\Pi r^{2}h$$ $$\Rightarrow \frac{1}{3} * \frac{22}{7} * 4 * 4 * \sqrt{132}$$ $$\Rightarrow \frac{362\sqrt{132}}{21}$$

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