Question : The arc length of a sector of a circle that subtends a $22.5^{\circ}$ angle at the centre is given as $16.5$ cm. What will be the radius (in cm) of the circle? [Use $\pi=\frac{22}{7}$]
Option 1: 35
Option 2: 49
Option 3: 42
Option 4: 48
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Correct Answer: 42
Solution :
Given: Length of a sector = $16.5$ cm
$\theta$ = $22.5^\circ$
We know that,
Length of the sector = $\frac{\theta}{360^\circ}×2\pi r$
⇒ $16.5 = \frac{22.5^\circ}{360^\circ}×2\pi r$
⇒ $16.5 = \frac{1}{16}×2\pi r$
⇒ $r = \frac{16×16.5×7}{2×22} = 42$ cm
Hence, the correct answer is 42.
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