The hour hand and minute hand of a clock are 4 cm and 5 cm respectively. find the difference between distances traversed by their extremities in 27 hours.
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Each of them describe a circular path.
The hour hand :
It makes one revolution in 12 hrs
In 27 hrs it makes :
27/12 = 2.25 revolutions.
In one revolution it covers :
3.142 × 2 × 4 = 25.136 cm
In 2.25 revolutions it covers :
2.25 × 25. 136 = 56.556cm
The minute hand :
In one revolution it takes 1 hr.
In 27 hrs it makes 27 revolutions.
Distance covered in one revolution is :
3.142 × 2 × 5 = 31.42 cm
In 27 revolutions it covers :
27 × 31.42 = 848.34cm
The difference of the distances covered is :
848.34 - 56.556 = 791.784 cm
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