Question : The area of a sector of a circle that subtends a 22.5° angle at the centre is given as 346.5 cm². What will be the radius (in cm) of the circle? [Use $\pi=\frac{22}{7}$]
Option 1: 35
Option 2: 45
Option 3: 42
Option 4: 48
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Correct Answer: 42
Solution : Given, Area = 346.5 cm$^2$ Angle ($\theta$) = 22.5° Let $r$ be the radius. Area $=\frac{\theta}{360°}\times \pi r^2$ ⇒ $346.5=\frac{22.5°}{360°}\times \frac{22}{7}\times r^2$ ⇒ $\frac{346.5\times360\times7}{22.5\times 22}=r^2$ ⇒ $r^2 = \frac{873180}{495}$ ⇒ $r^2=1764$ ⇒ $r=\sqrt{1764}$ ⇒ $r$ = 42 cm Hence, the correct answer is 42.
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