The ratio of the measure of the arc length and the circumference is proportional to the measure of the intercepted angle and one whole revolution. If we let x be the measure of the intercepted angle in degrees, the equation will become,
x/360 = 8 in/(2π(3 in))
The value of x from the equation when π = 22/7 is 152.72°.
To convert this value to radians, we use the dimensional analysis as shown below,
in radians = (152.72°)(2π/360°)
in radians = 2.7 radians
Thus, the answer is third choice.
