Question

The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. [Use $\pi =3.14)$

Answer 1

The lengths of the short hand and long hand are 4cm and 6cm respectively.
Short hand is hour hand. it completes one revolution in 12 hours.
Distance travelled by short hand of the clock in one revolution will be equal to the circumference of a circle with radius 4cm.
Distance travelled by short hand in one revolution (in 12 hours) is $2\times \pi \times 4=8\pi$
Distance travelled by short hand in 24 hours = $2\times 8\pi =16\pi$
Long hand is minute hand. it completes one revolution in 1 hour.
Distance travelled by long hand of the clock in one revolution will be equal to the circumference of a circle with radius 6cm.
Distance travelled by long hand in one revolution (in 1 hour) is $2\pi \times 6=12\pi$
Distance travelled by long hand in 24 hours =$24\times 12\pi =288\pi$
So, the sum of the distance travelled by their tips in one day = 288 $\pi$ + 16 $\pi$ = 304 $\pi$ cm