Question : The area of the sector of a circle of radius 12 cm is $32 \pi \;\mathrm{cm}^2$. Find the length of the corresponding arc of the sector.
Option 1: $\frac{16}{3} \pi$ cm
Option 2: $\frac{13}{3} \pi$ cm
Option 3: $\frac{10}{3} \pi$ cm
Option 4: $\frac{8}{3} \pi$ cm
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Correct Answer: $\frac{16}{3} \pi$ cm
Solution :
Given:
The radius of the circle is 12 cm.
The area of the sector of a circle is $32\pi$ cm
2
.
Area of the sector = $\pi r^2× \frac{\theta}{360^{\circ}}$
⇒ $32\pi=\pi ×12^2×\frac{\theta}{360^{\circ}}$
⇒ $\frac{\theta}{360}=\frac{32}{144}$
⇒ $\frac{\theta}{360}=\frac{2}{9}$
Length of the arc = $2\pi r×\frac{\theta}{360^{\circ}}$
= $2\pi×12×\frac{2}{9}=\frac{16}{3} \pi$ cm
So, the length of the arc is $\frac{16}{3} \pi$ cm.
Hence, the correct answer is $\frac{16}{3} \pi$ cm.
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