Question : The area of a sector of a circle is 66 cm2 and the angle of the sector is 60°. Find the radius of the circle.
Option 1: $5 \sqrt{15} \mathrm{~cm}$
Option 2: $6 \sqrt{14} \mathrm{~cm}$
Option 3: $7 \sqrt{19} \mathrm{~cm} $
Option 4: $3 \sqrt{14} \mathrm{~cm} $
Correct Answer: $3 \sqrt{14} \mathrm{~cm} $
Solution :
The area \(A\) of a sector of a circle with radius \(r\) and central angle \(\theta\) (in degrees),
$A = \frac{\theta}{360} \times \pi r^2$
Given that \(A = 66\;\mathrm{cm^2}\) and \(\theta = 60^{\circ}\).
$⇒66 = \frac{60^{\circ}}{360^{\circ}} \times \frac{22}{7} \times r^2$
$⇒66=\frac{11}{21}r^2$
$⇒r^2 = 126$
$⇒r^2=3\sqrt{14}\ \text{cm}$
Hence, the correct answer is $3\sqrt{14}\ \text{cm}$.
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