A sector of a circle of radius has an angle . By coinciding its straight edges a cone is formed. Find the volume of cone.
Step 1: Find the radius and height of the cone.
Radius of circle, .
Angle of sector,
The length of an arc is given as,
Circumference, of the circle, is given by:
Where is the radius of the base of the cone formed.
Length of an arc is the circumference of the base circle. So,
As, slant height of the cone is equal to the radius of the sector used form cone
Also, in a cone
Step 2: Find the volume of cone.
Volume of cone:
Hence, the volume of the cone is .