A circular sheet of radius 10cm is cut to from a sector of \(120^\circ\). What is the length of the arc of this sector?
A circular sheet of radius 10cm is cut to from a sector of \(120^\circ\). What is the length of the arc of this sector?
10 सेमी त्रिज्या वाली एक वृत्ताकार शीट को काटकर \(120^\circ\) का एक सेक्टर बनाया जाता है। इस सेक्टर की चाप (Arc) की लंबाई क्या होगी?
Detailed Solution & Logic
Correct Answer:
$\frac{440}{21} $cm/ सेंटीमीटर
Radius r = 10cm, angle = \(120^\circ\)
Arc length formula:
$L=\frac{\theta}{360}\times 2\pi r$
$L=\frac{120}{360}\times 2\pi\times 10$
$L=\frac{1}{3}\times 20\pi$
$L=\frac{20\pi}{3}$ cm
Using $\pi=\frac{22}{7}$:
$L=\frac{20}{3}\times \frac{22}{7}$
$L=\frac{440}{21}$ cm
✅ Answer: $\frac{440}{21}$ cm
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