Question

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.

Answer 1

Given:

Short hand (hour hand) length = 4 cm

Long hand (minute hand) length = 6 cm

Time = 2 days = 48 hours

Distance travelled by hour hand

Length = radius = 4 cm

Circumference =

2πr = 2π(4) = 8π cm

Hour hand completes 1 rotation in 12 hours.

`48/12`

= 4 rotations

4 × 8π = 32π cm

Distance travelled by minute hand

Length = 6 cm

2πr = 2π(6)

= 12π cm

Minute hand completes 1 rotation every hour.

48 rotations

48 × 12π

= 576π cm

Total distance travelled by both hands

32π + 576π

= 608π cm

If π = 3.14:

608 × 3.14

= 1908 cm