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

Question

Philoid · Accepted Answer

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.