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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Question : In a circle of radius 42 cm, an arc subtends an angle of 60° at the centre. Find the length of the arc. $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$
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Question : The area of the sector of a circle is 128 cm2. If the length of the arc of that sector is 64 cm, then find the radius of the circle.
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