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 (Take π = 3.14).

Answer 1

Given:

Short (hour) hand length = 4 cm; long (minute) hand length = 6 cm.

Time interval = 2 days = 48 hours.

Take π = 3.14.

Step-wise calculation:

1. Distance travelled by tip = (Number of revolutions) × (Circumference = 2πr).

2. Minute (long) hand r = 6 cm:

Revolutions in 48 hours = 48 (one per hour)

Distance = 48 × 2π(6)

= 48 × 12π

= 576π cm

Using π = 3.14:

= 576 × 3.14 

= 1808.64 cm

3. Hour (short) hand (r = 4 cm):

Revolutions in 48 hours = `48/12` = 4 (one full revolution every 12 hours).

Distance = 4 × 2π(4)

= 4 × 8π

= 32π cm

Using π = 3.14:

= 32 × 3.14 

= 100.48 cm

4. Sum of distances

= 1808.64 + 100.48 

= 1909.12 cm

The sum of distances travelled by the tips of the two hands in 2 days is 1909.12 cm.