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Question
The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14) ?
Solution
Let r and R be the lengths of the short and long hands of the clocks, respectively.
Length of the short hand of the clock, r = 4 cm
Distance travelled by the tip of the short hand in 12 hours = \[2\pi r\] = 2 × 3.14 × 4 = 25.12 cm
∴ Distance travelled by the tip of the short hand in 24 hours = 2 × 25.12 = 50.24 cm
Length of the long hand of the clock, R = 6 cm
Distance travelled by the tip of the long hand in 1 hour =\[2\pi R\]
2 × 3.14 × 6 = 37.68 cm
∴ Distance travelled by the tip of the long hand in 24 hours = 24 × 37.68 = 904.32 cm
Now,
Sum of the distances travelled by their tips in 24 hours
= Distance travelled by the tip of the short hand in 24 hours + Distance travelled by the tip of the long hand in 24 hours
= 50.24 cm + 904.32 cm
= 954.56 cm
Hence, the sum of the distances travelled by their tips in 24 hours is 954.56 cm.
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