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Question
Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.
Solution
Let the central angle of the sector be θ.
Given that, radius of the sector of a circle (r) = 5 cm
And arc length `(l)` = 3.5 cm
∴ Central angle of the sector,
θ = `("arc length" (l))/"radius"`
⇒ θ = `3.5/5` = 0.7R ...`[∵ θ = l/"r"]`
⇒ θ = `(0.7 xx 180/pi)^circ` ...`[∵ 1"R" = 180^circ/pi "D"^circ]`
Now, area of sector with angle θ = 0.7
= `(pi"r"^2)/360^circ xx (0.7) xx 180^circ/pi`
= `(5)^2/2 xx 0.7`
= `(25 xx 7)/(2 xx 10)`
= `175/20`
= 8.75 cm2
Hence, the required area of the sector of a circle is 8.75 cm2.
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