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The arc of a circle 50 cm long, subtends angle of 75° at the center of…

The arc of a circle 50 cm long, subtends angle of 75° at the center of the circle. Find correct to 3 significant figures, the radius of the circle. Take (pi = frac{22}{7})

  • A.
    8.74cm
  • B.
    38.2cm
  • C.
    61.2cm
  • D.
    76.4cm
Correct Answer: Option B
Explanation

Length of arc = (frac{theta}{360} times 2pi r)

(50 = frac{75}{360} times 2 times frac{22}{7} times r)

(r = frac{50 times 360 times 7}{75 times 2 times 22})

(r = frac{420}{11})

= 38.18 cm (approxeq) 38.2 cm (3 sig. figs)

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