Question

A sector of a circle of radius 12 cm has an angle ${120}^0$. By coinciding its straight edges a cone is formed. Find the volume of cone.

Answer 1

Given the radius of circle $12cm$

This becomes the slant height of cone

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

The length of arc is given as= $\frac{x}{360}\times 2\pi r\frac{120}{360}\times 2\times \pi \times 12\frac{1}{3}2\pi \times 122\pi \times 48\pi$

This become the circumference of base circle= $2\pi r=8\pi 2r=8r=4$

According to Pytagorous theorm

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

Volume of cone$=\frac{1}{3}\pi r^{2}h\frac{1}{3}\times \frac{22}{7}\times 4\times 4\times \sqrt{132}\frac{362\sqrt{132}}{21}$