The central angle theta is subtended by the arc of length S

The central angle theta is subtended by the arc of length S = 6 cm on a circle of radius 2cm what is the area of the sector?

Solution

We have given Arc length s=6cm and radius r=2cm

central angle Theta =s/r=6/2=3 radians

converting radians into degrees

Theta =3radians =171.8874 degrees

Area of the Sector =(theta/360⁰)*(pi)*r² =((171.8874)/360⁰)*(pi)*(2)²

Area of the Sector = ((171.8874)/360⁰)*(pi)*4 =(0.477465)*(pi)*4=6

Area of the Sector =6 cm²