Question

The minute hand on a clock is 9 centimeterslong and travels through an arc of 252° every 42 minutes. To the nearest tenth of a centimeter, how far does the minute handtravel during a 42-minute period?

Answer 1

Answer: the minute hand travel 39.6 cm

Explanation:

Length of minute hand of a clock = 9 cm

Central angle made by the minute hand = 252°

To find: how far the minute hand travel

Therefore

Length of minute hand is equal to the radius of circle

As we know the circumference of a circle is given by

`C= 2\pi r (\theta)/(360^\circ)` where C is circumference , r is radius and ∅ is the central angle

So we have

`C= 2 * (22)/(7) * 9 * (252^\circ)/(360^\circ) \\\\\Rightarrow C= 2 * (22)/(7) * (252^\circ)/(40^\circ) \\\\\Rightarrow C= (11)/(7) * (252^\circ)/(10^\circ) = 39.6`

Hence, the minute hand travel 39.6 cm in 42 minute period