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Find the area of the sector of a circle of radius \[5\] cm, if the corresponding arc length is \[3.5\] cm.
Find the area of the sector of a circle of radius \[5\] cm, if the corresponding arc length is \[3.5\] cm.
Areas Related to Circles | Exercise 11.4 | Maths | NCERT Exemplar
Find the area of the sector of a circle of radius \[5\] cm, if the corresponding arc length is \[3.5\] cm.

solution

Given Radius of the circle = r = \[5\] cm

Given Arc length of the sector = l = \[3.5\] cm

Let us consider the central angle (in radians) be \[\theta \].

As we know that Arc length = Radius × Central angle (in radians)

From Central angle (\[\theta \])= Arc length / Radius = l / r = \[3.5/5\] = \[0.7\] radians

As we know that the Area of the sector = \[(1/2)\times {{r}^{2}}\theta \] = \[(1/2)\times 25\times 0.7\] = \[8.75\] \[c{{m}^{2}}\]

Therefore, the required area of the sector of a circle is \[8.75\] \[c{{m}^{2}}\].

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