Final answer:
To find the arc length, calculate 2/3 of the circumference of the circle (2πr) since the central angle is 240° out of 360°. With a radius of 2 inches, the total circumference is 12.56636 inches, making the arc length 8.37758 inches, which rounds to 8.37 inches.
Step-by-step explanation:
The question asks to determine the length of the arc in a circle where the central angle (θ) is 240° and the radius is 2 inches. To calculate the arc length, we use the formula for the circumference of a circle which is 2πr (where π is approximately 3.14159 and r is the radius), and then find the fraction of the circumference that corresponds to the central angle.
There are 360 degrees in a full circle, so a central angle (θ) of 240° represents 240/360 or 2/3 of a full revolution. Therefore, the arc length (S) is 2/3 of the total circumference. Using the formula for circumference (C = 2πr), and knowing the radius (r) is 2 inches, we find C = 2 * 3.14159 * 2 inches = 12.56636 inches. The arc length S is then 2/3 * 12.56636 inches = 8.37758 inches, which we can round to 8.37 inches for the purpose of selecting an answer from the given options. Therefore, the length of the arc is 8.37 inches (option b).