The Central Angle of the sector in radians is 0.3184 π .
In the question ,
it is given that ,
the radius of the sector = 24 m
the area of the sector = 288 m²
we know that the Area of the sector of the circle is given by the formula
Area = πr²(θ/360)
Substituting the values , we get
288 = (3.14)*(24)²*(θ/360)
θ = (288*360)/((3.14)*(24)²)
θ = 1,03,680/1808.64
θ = 57.32°
converting the angle to radian ,
we get
θ = 57.32° × π/180 radian
= 0.3184 π
Therefore , The Central Angle of the sector in radians is 0.3184 π .
The given question is incomplete , the complete question is
A sector of a circle of radius 24 m has an area of 288 m² . find the central angle of the sector in radians .
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