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. $[ take\ \pi=\frac{22}{7} ]$.

Given: The short and long hands of a clock are $4\ cm$ and $6\ cm$ long respectively.

To do: To find the sum of distances travelled by their tips in 2 days. 

Solution:

The tips of clock cover circular paths.

The hour hand covers 4 complete circles in 2 days              $( 48\ hours)$

Here $r=4\ cm$

Distance $= 4\times( 2\pi r)=2 \times \frac{22}{7} \times 4 \times 4 = 100.57\ cm$

The minute hand covers $= 48$ Circles in $2$ days              $( Each\ hour = 1\  circle)$

Here $r=6\ cm$

Distance $= 48\times( 2\pi r)=2 \times \frac{22}{7} \times 6 \times 48 = 1810.23\ cm$

Total distance $= 100.57 + 1810.23 = 1910.8\ cm$
 

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Updated on: 10-Oct-2022

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