A sector of circle of radius 3 cm has an angle of 120°. If it is modulated into a cone, find then  volume of the cone is

When a sector  modulated into cone

 Length of the sector $=$ circumference of the base of the cone

$\frac{120°}{360°}\times 2\pi \left(3\right)=2\pi r$

$r=1cm$ (radius of the base of the cone)

Slant height of the cone$=$ radius of the sector

$\therefore l=3cm$

Then $h=\sqrt{l^2-r^2}=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}$

Volume of the cone $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \pi {\left(1\right)}^{2}2\sqrt{2}=\frac{2\sqrt{2}\pi }{3}$