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Sum

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

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#### 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, `theta = ("arc length" (l))/"radius"`

⇒ `theta = 3.5/5` = 0.7R .....`[because theta = l/r]`

⇒ `theta = (0.7 xx 180/pi)` .....`[because 1R = 180^circ/pi D^circ]`

Now, area of sector with angle θ = 0.7

= `(pir^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 cm^{2}

Hence, the required area of the sector of a circle is 8.75 cm^{2}.

Concept: Areas of Sector and Segment of a Circle

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