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
waec 2000mathematics

The correct answer is B. 38.2cm

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

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

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

\(r = \frac{420}{11}\)

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

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