Question : In a circle of radius 14 cm, an arc subtends an angle of 90° at the centre. The length of are (in cm) is equal to: (Take $\pi=\frac{22}{7}$)
Option 1: 22
Option 2: 18
Option 3: 20
Option 4: 24
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Correct Answer: 22
Solution :
The length of an arc in a circle, where \(\theta\) is the angle that the arc subtends at the centre of the circle and \(r\) is the radius of the circle.
$ = \frac{\theta}{360} \times 2\pi r$
Substituting the given values,
The length of an arc in a circle,
$ = \frac{90^\circ}{360^\circ} \times 2 \times \frac{22}{7} \times 14$
$ = 22 \, \text{cm}$
Hence, the correct answer is 22.
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