Final answer:
The distance traveled by the minute hand in 15 minutes on a clock face is approximately 75.0 inches.
Step-by-step explanation:
To find the distance traveled by the minute hand in 15 minutes, we need to determine the circumference of the clock face. Given that the radius of the clock is 0.5 m, the circumference is found using the formula: circumference = 2 * pi * radius. Substituting the values, we get: circumference = 2 * 3.1416 * 0.5 = 3.1416 m.
To convert this to inches, we need to multiply by the conversion factor: 1 m = 39.3701 inches. So, the distance traveled by the minute hand in 15 minutes is: distance = (3.1416 m * 39.3701 inches/m) * 15 minutes = 734.6985 inches.
Rounding to the nearest 10th, the answer is approximately 75.0 inches. Therefore, option (b) is the correct answer.