Answer
29.2°
Explanation
Given in the question,
radius of circle = 4 m
area of sector = 5π m²
The area of a sector of a circle is
½ r² ∅
where r is the radius and ∅ the angle in radians subtended by the arc at the centre of the circle.
area of a sector = ½ r² ∅
5π = ½ r² ∅
5π * 2 = r² ∅
10π = r² ∅
10π = 4² ∅
10π = 16∅
∅ = 16 / 10π
∅ = 8/5π in radians
Converting rad to degree
π = 180°
1rad = 180/π
8/5π rad = 8/5π * 180/π
= 8/5π × 180/π
= 29.2°
