Question : A sector of a circle has a central angle of 45° and an arc length of 22 cm. Find the radius of the circle. ( Use $\pi=\frac{22}{7}$)
Option 1: 32 cm
Option 2: 35 cm
Option 3: 28 cm
Option 4: 36 cm
Correct Answer: 28 cm
Solution :
Given: Central angle = $45^\circ$
Arc length = 22 cm
We know that,
Length of the arc = $\frac{\theta}{360^\circ}\times2\pi r$
⇒ $22=\frac{45^\circ}{360^\circ}\times2\times\frac{22}{7}\times r$
⇒ $22=\frac{1}{8}\times2\times\frac{22}{7}\times r$
⇒ $r=7\times4$
⇒ $r=28$ cm
Hence, the correct answer is 28 cm.
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