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MatroZZZ [7]
3 years ago
7

In one day, by how much does the distance traveled by the tip of the minute hand exceed the distance traveled by the tip of the

hour hand?
Mathematics
1 answer:
lidiya [134]3 years ago
7 0
In one day, there are 24 hours. In 1 hour, there are 3,600 seconds. So, that means that there are 86,400 seconds. Also, in 1 day, the short hand which denotes the number of hours, makes 2 revolutions around the clock. Its distance traveled would be twice the perimeter of the circle. 

Distance traveled by hour hand = 2(2πr) = 4πr₁

In 60 s, the long hand, which denotes numbers of minutes, makes one revolution around the clock. Since there are 86,400 seconds in a day, that would be a total of 1,440 revolutions.

Distance traveled by minute hand = 1,440(2πr) = 2,880πr₂

Difference = 2880πr₂ - 4πr₁ = 4π(720r₂ - r₁), where r₁ is the length of hour hand and r₂ is the length of minute hand.
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