The short and long hands of a clock are 4 cm and 6 cm long respectivel

1.	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 pi = 3.14]
Answer» The short and long hands of a clock are 4 cm and 6 cm long respectively. In an hour the hour hand completes one rotation in 12 hours therefore in 24 hours it will complete 2 rotations. Similarly, the minute hand completes one rotation therefore in 24 hours the minute hand will complete 24 rotations. Distance travelled by its tip in 2 days = 4(circumference of the circle with radius 4 cm) = (4 × 2π × 4) cm = 32π cm (As, in 2 days, the short hand will complete 4 rounds) In 2 days, the long hand will complete 48 rounds length moved by its tip = 48(circumference of the circle with radius 6 cm) = (48 x 2π x 6) cm = 576 π cm Now, Sum of the lengths moved = (32π + 576π) = 608π cm = (608 x 3.14) cm = 1909.12 cm

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 pi = 3.14]

Answer»

The short and long hands of a clock are 4 cm and 6 cm long respectively.

In an hour the hour hand completes one rotation in 12 hours therefore in 24 hours it will complete 2 rotations.

Similarly, the minute hand completes one rotation therefore in 24 hours the minute hand will complete 24 rotations.

Distance travelled by its tip in 2 days = 4(circumference of the circle with radius 4 cm)

= (4 × 2π × 4) cm = 32π cm

(As, in 2 days, the short hand will complete 4 rounds)

In 2 days, the long hand will complete 48 rounds length moved by its tip = 48(circumference of the circle with radius 6 cm)

= (48 x 2π x 6) cm

= 576 π cm

Now,

Sum of the lengths moved

= (32π + 576π)

= 608π cm

= (608 x 3.14) cm

= 1909.12 cm