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: Option A
Explanation
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)