Question

the long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of distances travelled by their tips in 24 hours . ( use π = 3.14 )

Answer 1

The length of the hands will be the radius of the circle which they form while moving. So, the distance covered by their tip would be equal to the circumference of the circle they form.

We know that, circumference of circle = 2πr

So, for the first hand, distance travelled = circumference = 2πr

r = 6 cm

= 2 π × 6

= 2 × 3.14 × 6

= 37.68 cm

Now, the longer hand is the minute hand, in 24 hrs, the revolution made by it = 24 times. Hence, total distance covered = 37.68 × 24 = 904.32

Now, for the second hand, distance travelled = 2πr

= 2 × 3.14 × 4

= 25.12 cm

Now the hour hand completes 2 revolution in 24 hrs. Hence total distance

= 25.12 × 2

= 50.24

So, their sum = 904.32 + 50.24

= 954.56 cm

= 9.5456 m

Answer :- 954.56 cm or 9.5456 m

Answer 2

Question :

the long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of distances travelled by their tips in 24 hours . ( use π = 3.14 )

Answer:

The distance travelled will be 954.56 cm .

Step-by-step explanation:

The short hand will complete 2 revolutions in 24 hours.

Distance travelled will be = circumference of the circle with radius .

Radius of the short hand = 4 cm.

C = 2 π r

= > C = 2 π × 4 cm

= > C = 8 π cm .

We will keep it in π for some time .

Now since the short hand circles twice :

C = 2 × 8 π cm

= > C = 16 π cm

The long hand is the minute hand .

Now the long hand will rotate 24 times .

C = 2 π r

= > C = 2 π × 6 cm

= > C = 12 π cm .

C = 12 π cm × 24 since the hand rotates 24 times .

= > C = 288 π cm

Now the sum of distances = 288 π cm + 16 π cm

                                            = 304 π cm

                                            = 304 × 3.14 cm

                                            = 954.56 cm

The distance travelled will be 954.56 cm .