Question

Area of segment with central angle 20° and radius 2r​

Answer 1

Answer:

Question:

Given a central angle of {eq}20 ^\circ {/eq} and a circle of radius {eq}2 {/eq}, determine the area of the sector and arc length defined by the central angle.

Area of a Sector of a Circle:

The area of a sector of a cirle is equal to half the product of the square of the radius (r) and the central angle {eq}(\theta) {/eq} in radians. This means that if the central angle is in degrees it has to be converted into radians by multiplying it with the simplified conversion factor of {eq}\frac {\pi \text{ rad}}{180^\circ} {/eq}.