Question

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

Answer 1

Step 1: Given data
Radius $r=$ minute hand of clock= $1.5$ cm

Step 2: Finding angle $\theta$
Now we know that minute hand makes $1$ revolution in $1$ hour.
Hence, we can say that minute hand completes ${360}^{\circ }$ in one hour.
So, degree completed in one minute $=\frac{{360}^{\circ }}{60}$
Hence $\theta ={240}^{\circ }$
$\Rightarrow \theta =240\times \frac{\pi }{{180}^{\circ }}=\frac{4\pi }{3}$

Step 3: Solve for length of arc $\left(l\right)$
$l=r\theta$
$\Rightarrow l=1.5\times \frac{4\pi }{3}$
$\Rightarrow l=0.5\times 4\pi =2\pi$
$\Rightarrow l=2\times 3.14$
$\Rightarrow l=6.28$ cm