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
Correct answer is A
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)