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A clock's hour hand is 4 inches long, and its minute hand is 6 inches long. How many inches

does the point of each hand travel in 24 hours?

User Elenita
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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).

User Zalika
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