The short and long hands of a clock are 4 cm and 6 cm long respectively.
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.

Solution:

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

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

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 $=48 \times 2 \pi \times 6=576 \pi \mathrm{cm}$

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

$=32 \pi+576 \pi$

$=608 \pi$

$=608 \times 3.14$

$=1909.12 \mathrm{~cm}$

 

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