The minute hand of a watch is 1.5 cm long. How far does its tip move in 40 minutes?

Concept:

If the arc of a circle whose radius is r units subtends an angle θ at the centre of the circle, then the length of the arc is given by: l = r × θ .

Calculation:

Given: l = 1.5 cm and Tip move in 40 minutes

In 60 minutes, the minute hand of a watch completes one revolution. Therefore, in 40 minutes, the minute hand turns through \(\rm 2\over3\) of a revolution.

Then, θ = \(\rm 2\over3\) × 360° or \(\rm \frac {4π}{3}\) radian.

Hence, the required distance travelled is given by  

As we know that, 180° = π radian

⇒ 60° = π / 3

As we know that, l = r × θ

⇒ l = 1.5 × \(\rm \frac {4π}{3}\)

⇒ l = 2π 

⇒ l = 2 × 3.14 cm

⇒ l = 6.28 cm