Question : In a circle, an arc subtends an angle of 84° at the centre. If the length of the arc is 22 cm, then the radius of the circle (in cm) is equal to: Take $\pi=\frac{22}{7}$
Option 1: 19
Option 2: 15
Option 3: 17
Option 4: 13
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Correct Answer: 15
Solution : The angle subtended by an arc at the centre = $84^\circ$ Length of given arc = 22 cm Let the radius of the circle be $r$. We know, length of arc = $\frac{\theta}{360^\circ}\times 2\pi r$ As per given condition, $\frac{84^\circ}{360^\circ}\times 2 \pi r = 22$ ⇒ $\frac{84}{360}\times 2 \times \frac{22}{7}×r = 22$ ⇒ $r= \frac{360\times 7}{2\times 84}=15$ cm Hence, the correct answer is 15.
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