Final answer:
The point of the hour hand travels approximately 50.265 inches, and the point of the minute hand covers approximately 904.778 inches in 24 hours.
Step-by-step explanation:
The question is about calculating the distance traveled by the point of each hand of a clock in 24 hours. Given that the hour hand is 4 inches long, and the minute hand is 6 inches long, we can use the formulas for the circumference of a circle (C = 2πr) to determine the distance each hand travels.
The hour hand completes 2 full cycles in 24 hours, and the minute hand completes 24 full cycles. Thus, the distance traveled by the point of the hour hand is 2 ⋅ (2π ⋅ 4 inches) and the distance traveled by the point of the minute hand is 24 ⋅ (2π ⋅ 6 inches).
The final calculations yield the distances traveled:
Hour hand: 2 ⋅ (2π ⋅ 4 inches) = 50.265 inches (approximately).
Minute hand: 24 ⋅ (2π ⋅ 6 inches) = 904.778 inches (approximately).