Question

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

Answer 1

Hint:
Total distance travelled will be equal to distance travelled in one revolution that will it’s circumference multiplied by total revolution. You have to add distance travelled by short hand and distance travelled by long hand.

Complete step-by-step answer:

In two days total distance covered will be equal to distance covered by shorthand + distance covered by long hand of clock.
Distance covered by small hand or hour hand tip = total revolution \[ \times 2\pi r\]
=$\frac{{2 \times 24}}{{12}} \times 2 \times 3.14 \times 4 = 100.48{\text{cm}}$(in two days total hours is 48 and hour hand completes one revolution in 12 hours so you have to divide by 12 to find total revolution)
Distance travelled by large hand or minute hand tip =total revolution $ \times 2\pi {\text{r}}$
$ \Rightarrow \frac{{2 \times 24}}{1} \times 2 \times 3.14 \times 6 = 1808.64{\text{cm}}$
In two days total hours is 48 and a minute hand completes one revolution in 1 hour so to find the total number of revolutions you have to divide by 1.
So total distance covered= 100.48cm + 1808.64cm=1909.12cm

Note: -Whenever you get this type of question the key concept of solving is you have to find total distance covered by short hand and total distance covered by long hand and add them to find total distance travelled. And to find the total number of revolutions you have to count the total number of hours and divide by as much number of hours in which that hand completes one revolution.