Question

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

Answer 1

In 2 days, the short hand will complete 4 rounds.
Length of the short hand = 4 cm

Distance covered by the short hand = $4\times 2\mathrm{\pi }\times 4=32\mathrm{\pi }\mathrm{cm}$

In the same 2 days, the long hand will complete 48 rounds.
Length of the long hand = 6 cm
Distance covered by the long hand = $48\times 2\mathrm{\pi }\times 6=576\mathrm{\pi }\mathrm{cm}$

∴ Total distance covered by both the hands = Distance covered by the short hand + Distance covered by the long hand

$$\begin{gathered} =32\mathrm{\pi }+576\mathrm{\pi } \\ =608\mathrm{\pi } \\ =608\times 3.14 \\ =1909.12\mathrm{cm} \end{gathered}$$