In the diagram O is the center of the circle. Reflex angle XOY = 210^\circ and the length of the minor arc is 5.5m. Find, correct to the nearest meter, the length of the major arc.
Attached Figure / Diagram
A
8m
B
9m
C
10m
D
13m
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Given, Length of minor arc = 5.5m
Angle subtended by minor arc = 360^\circ - 210^\circ = 150^\circ
\(\therefore 5.5 = \frac{150}{360} \times 2 \times \frac{22}{7} \times r \)
\(\frac{55r}{21} = 5.5\)
\(r = \frac{5.5 \times 21}{55}\)
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)
Source: Myschool Past Questions Archive (Record #26511)