In the diagram above, O is the centre of the circle. Reflex angle XOY = 210º and the length of the minor arc is 5.5m. Find, correct to the nearest metre the length of major arc.
Attached Figure / Diagram
A
8m
B
9m
C
10m
D
13m
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Length of arc = \(\frac{Ø}{360} \times 2\pi\)
5.5 = \(\frac{360 - 210}{360}\) x 2 x \(\frac{22}{7}\)
\(\frac{ 5.5 \times 360\times7}{150\times2\times22}\) = 2.1
length of major arc = \(\frac{210}{360}\) x 2 x \(\frac{22}{7}\) x 2.1
7.7m ≈ 8m
Source: Myschool Past Questions Archive (Record #70133)