Question

The hour and minute hands of a clock are 4 cm and 6 cm long respectively. Find the sum of the distances travelled by their tips in 2 days.

Answer 1

The radius of the path inscribed by the hour hand = Length of the hour hand = 4 cm
The radius of the path inscribed by the minute hand = Length of the minute hand = 6 cm

The circumference of the path inscribed by the hour hand = $2\mathrm{\pi }r=2\times \frac{22}{7}\mathrm{x}4=\frac{176}{7}\mathrm{cm}$.
The hour hand makes 2 revolutions in one day.
∴ The distance covered by the hour hand in 2 days = $\frac{176}{7}\times 2\times 2=100.57\mathrm{cm}$.
The distance covered by the minute hand in 1 revolution = $2\mathrm{\pi r}=2\times \frac{22}{7}\mathrm{x}6=\frac{264}{7}\mathrm{cm}$
The minute hand makes 1 revolution in one hour.
∴ In 1 day, it makes 24 revolutions.
In 2 days, it makes 2 x 24 revolutions.
∴ ​The distance covered by the minute hand in ​2 days = $\left(2\times 24\times \frac{264}{7}\right)\mathrm{cm}=\left(\frac{12672}{7}\right)\mathrm{cm}=1810.28\mathrm{cm}$
The sum of the distances travelled by the hour and minute hands in 2 days = 1810.28 + 100.57 = 1910.85 cm.