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

Solution:

Given,

The minute hand of a watch = 1.5 cm.

We know the arc length is given by,

l = rθ.

Now we know that minute make 1- a revolution in 1 hour,

Hence we can say the minute hand completes 360° in 1 hour

θ= 360°.

r = 1.5 cm.

So degree completed in

1 min = 360/60.

So degree completed in

40 min = 360/60 × 40 = 240°.

θ = 240°.

Radian measure = π/180 × θ.

= π/180 × 240.

= 4π/3.

Now, l = rθ.

l = 1.5 × 4π/3.

l = 0.5 × 4π.

l = 2π.

l = 2 × 3.14

l = 6.28 cm.

Therefore, l = 6.28 cm.

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

Summary:

The minute hand of a watch is 1.5 cm long. The tip moves 6.28 cm along in 40 minutes.