The Central angle of Sector is 305.73° . The Central angle of sector is defined as the angle formed by two radii.
The Sector Area of a circle is the amount of space enclosed within the sector boundary. A sector always starts from the center of the circle. A circle sector is defined as the portion of the circle bounded between two radii and their adjacent arcs.
Mathematically, A = (θ/360°) × π r²
where, A---> area of sector of circle
θ----> Central angle of sector
r ----> radius of circle
pi (π) = 3.14
we have, Radius of circle (r) = 3 inch
Area of sector of circle (A) = 24 inch²
we have to find out the value of central angle of Sector .
putting the values in above formula we get,
24 = (θ/360°) × 3.14 ×(3)²
=> θ/360° = 24/28.26 = 0.849
=> θ = 360×0.849 = 305.73°
Hence, Central angle of sector is 305.73° ..
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