Question

What is the area of the sector of a circle of radius 5cm, which is formed by an arc of length 3.5cm?

Answer:

Area of the sector is 8.75 sq cm.

We are given that the length of the arc is 3.5 cm and the radius of the circle is 5 cm.
Therefore,
2πr*θ/360 = 3.5
⇒ 2πr*(θ/360)*r/2 = 3.5*r/2 (Multiplying both sides by r/2)
⇒ πr²(θ/360) = 3.5*2.5 = 8.75 sq cm
As we know πr²(θ/360) is the area of a sector with angle θ, we can conclude that area of the sector is 8.75 sq cm.


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