Question

The minute hand and the hour hand of a clock are $14$ cm and $7$ cm long respectively The total distance covered by their tips in one day is

• A. $24m$
• B. $26m$
• C. $22m$
• D. None of these

Answer 1

Answer: (C)

$22m$

In one day the minute hand covers 24 rounds while the hour hand covers 2 rounds
Let radius of circular path covered by minute hand : R = 14 cm
and radius of circular path covered by hour hand : r = 7 cm
Total distance travelled = $24\times 2\pi R+2\times 2\pi r$
= $48\pi R+4\pi r$
= $4\pi (12\times 14+7)cm$
= $4\times \frac{22}{7}\times 175$ cm
= 2200 cm = 22 m