Q8 of 59 Page 132

Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.

Radius of the circle = r = 5 cm


Arc length of the sector = l = 3.5 cm


Let the central angle (in radians) be θ.


As, Arc length = Radius × Central angle (in radians)


∴ Central angle (θ) = Arc length / Radius = l / r = 3.5/5 = 0.7 radians


Now, Area of the sector = (1/2) × r2θ = (1/2) × 25 × 0.7 = 8.75 cm2


Hence, required area of the sector of a circle is 8.75 cm2.


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