A circular jogging track has a radius of 50 m. A runner covers a curved path that subtends an angle of $120^\circ$ at the center. What is the length of the arc she runs?
A circular jogging track has a radius of 50 m. A runner covers a curved path that subtends an angle of $120^\circ$ at the center. What is the length of the arc she runs?
एक वृत्ताकार जॉगिंग ट्रैक की त्रिज्या 50 मीटर है। एक धाविका एक वक्र पथ पर दौड़ती है जो केंद्र पर $120^\circ$ का कोण बनाता है। उसने जो चाप (arc) तय किया, उसकी लंबाई क्या है?
Detailed Solution & Logic
Correct Answer:
$\frac{100\pi}{3}$ m
- Radius (r) = 50 m
- Angle = $120^\circ$
Arc length का formula:
$ \text{Arc length} = \frac{\theta}{360^\circ} \times 2\pi r $
मान रखते हैं:
$ \text{Arc length} = \frac{120}{360} \times 2\pi \times 50 $
$ = \frac{1}{3} \times 100\pi $
$ = \frac{100\pi}{3} \text{ m} $
सही उत्तर: $\frac{100\pi}{3}$ m
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