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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