In the diagram O is the center of the circle. Reflex angle XOY = 210° and the length of the minor arc is 5.5m. Find, correct to the nearest meter, the length of the major arc.

  • A 8m
  • B 9m
  • C 10m
  • D 13m
waec 2002mathematics

The correct answer is A. 8m

Given, Length of minor arc = 5.5m

Angle subtended by minor arc = 360° - 210° = 150°

\(\therefore 5.5 = \frac{150}{360} \times 2 \times \frac{22}{7} \times r \)

\(\frac{55r}{21} = 5.5\)

\(r = \frac{5.5 \times 21}{55}\)

r = 2.1m

Length of major arc = \(\frac{210}{360} \times 2 \times \frac{22}{7} \times 2.1\)

= \(7.7m \approxeq 8m\) (to the nearest metre)

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