Question

The hour and minute hands of a clock are 4.2 cm and 7 cm long respectively. Find the sum of the distances covered by their tips in 1 day.

Answer 1

Length of the hour hand (r)= 4.2 cm.
Distance covered by the hour hand in 12 hours = $2\mathrm{\pi r}$ = $\left(2\times \frac{22}{7}\times 4.2\right)$ cm = 26.4 cm

∴ Distance covered by the hour hand in 24 hours = (2 × 26.4) = 52.8 cm
Length of the minute hand (R)= 7 cm
Distance covered by the minute hand in 1 hour = $2\mathrm{\pi R}$ = $\left(2\times \frac{22}{7}\times 7\right)$ cm = 44 cm

∴ Distance covered by the minute hand in 24 hours = (44 × 24) cm = 1056 cm

∴ Sum of the distances covered by the tips of both the hands in 1 day = (52.8 + 1056) cm
= 1108.8 cm