An arc of a circle of length 22 cm subtends an angle of 3x^\circ at the center of the circle. Find the value of x if the diameter of the circle is 14 cm
A
60o
B
120o
C
180o
D
30o
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Length of an arc = \(\frac{\theta}{360}\) x 2\(\pi\)r
22 = \(\frac{3x}{360}\) x \(\frac{22}{7}\) x 7 (since D = 2r)
22 x 7 x 360 = 3x X 22 X 7
x = \(\frac{22 \times 7 \times 360}{3 \times 22 \times 7\times 2}\) = 60º
Source: Myschool Past Questions Archive (Record #7948)