Question : The area of a sector of a circle of radius 28 cm is 112 cm2. Find the length of the corresponding arc of the sector.
Option 1: 4 cm
Option 2: 8 cm
Option 3: 6 cm
Option 4: 5 cm
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Correct Answer: 8 cm
Solution :
Given: The area of a sector of a circle of radius 28 cm is 112 cm
2
.
The area of a sector of a circle of radius $r=\pi\times r^2 \times \frac{\theta}{360^\circ}$
⇒ $\frac{22}{7} \times 28^2 \times \frac{\theta}{360^\circ} = 112$
⇒ $\theta = \frac{360^\circ}{22}$
So, the length of the arc of the sector
$=2 \pi r × \frac{\theta}{360^\circ}$
$=2 \times \frac{22}{7} \times 28 \times \frac{360^\circ}{22 × 360^\circ}$
$= 8$ cm
Hence, the correct answer is 8 cm.
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