Question

The minute hand of a watch is $1.5 \,cm$ long. How far does its tip move in $40$ minutes? (Use $\pi = 3.14$)

• A. $2.68\,cm$
• B. $6.28\,cm$
• C. $6.82\,cm$
• D. $7.42\,cm$

Answer 1

Answer: (B)

$6.28\,cm$

Answer 2

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.