Question 1198595
A circular sector has a radius of 20 in. and a central angle of 120°. If this sector is cut out of paper and rolled so as to form the lateral surface of a right circular cone, find the total area and volume of the cone.


The central angle is 120 deg
radius = 20 in

length of arc = {{{theta/360}}}*2*pi*r

= 120/360 *2*20*pi
=40 *pi/3
When it is rolled into a cone the radius beomes the slant height and length of arc beomes circumference 0f the base of cone

2*pi*r = 40 *pi/3
r = 40/6 =20/3

height = sqrt(20^2-(20/3)^2 )

Volume of cone = 1/3  pi*r^2
height of cone = sqrt(20^2-(20/3)^2)

height h ={{{40*sqrt(2)/3}}} 
radius r=20/3
slant height l=20 
Find volume and Total surface area