Question

The distance between 6.00 A.M. and 3.15 P.M. by the tip of the 12 cm long hour hand in a clock is..in maths
​

Answer 1

Given :

Hour hand is 6 cm long.

To find :

The distance covered between 6.00 am and 3.15 pm by the tip of the 12 cm long hour hand.

Solution :

Difference between 6.00 and 3.15

is of 9.15 hr's

1 hour = 60 min

9.15 hours = 9.15 * 60

ie. 9.15 hours = 549 min

We know , 1 min = 1/2°

∴ 549 min = 549/2°

θ = (θ * π/180)

(549/2)° = (549/2)° * π/180

61π/20

Length of arc(s) = θ * r

hence radius of the arc, ie.12cm

length of arc(s)  = 61π/20 * 12

length of arc(s) = 183π/5 cm

Distance covered by the tip of hour hand = length of the arc

distance covered = 183π/5 cm

∴ The distance covered by the trip of the hour hand is 183π/5 cm