An arc of a circle, radius 14cm, is 18.33cm long. Calculate to the nearest degree, the angle which the arc subtends at the centre of the circle. [T = \(\frac{22}{7}\)]
A
11o
B
20o
C
22o
D
75o
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Length of an arc = \(\frac{\theta}{360} \times 2\pi r\)
18.33 = \(\frac{\theta}{360} \times 2 \times \frac{22}{7} \times 14\)
\(\theta = \frac{18.33 \times 360 \times 17}{2 \times 22 \times 14}\)
= 75o (approx.)
Source: Myschool Past Questions Archive (Record #36382)