Question

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

Answer 1

HINT:- Before solving this question, we must know the following terms:-
CIRCUMFERENCE: The circumference of a circle is defined as the linear distance around it. In other words, it is the perimeter of the circle.

Complete step-by-step solution -
The formula to find circumference of a circle is \[2\pi r\] .
HOUR HAND (Short hand)
The hour hand of a clock is the short hand.
The short hand of a clock completes 2 rounds in 1 day.
Therefore, it will complete 4 rounds in 2 days.
Thus, the distance travelled by it in 2 days would be:-
\[4\times 2\times \dfrac{22}{7}\times 4\ cm\]
\[\dfrac{704}{7}\ cm\]
MINUTE HAND (LONG HAND)
The minute hand of a clock is the long hand.
The long hand of a clock completes 24 rounds in 1 day.
Therefore, it will complete 48 rounds in 2 days.
Thus, the distance travelled by it in 2 days would be:-
\[\begin{array}{*{35}{l}}
   48\times 2\times \dfrac{22}{7}\times 6\ cm \\
   \dfrac{12672}{7}\ cm \\
\end{array}\]
SUM OF THE DISTANCES TRAVELED IN 2 DAYS
\[\dfrac{704}{7}+\dfrac{12672}{7}=\text{ }1910.85\text{ }cm\]
Therefore, the sum of the distances travelled by the tips of the hour and minute hands of the clock in 2 days is 1910.85 centimeter.

NOTE:- The student must do all the calculations for this question very carefully.
Any calculus error can make the calculations wrong because of which the answer would come out to be wrong.
Also, one must remember that a day has 24 hours and all other basic conversions as they can be included in a lot of questions.