The minute band of a watch is 1.5 cm long. How far does its tip move in 40 minutes ? (Use `pi` = 3 . 14)

Answer

To solve the problem of how far the tip of the minute hand moves in 40 minutes, we can follow these steps:

### Step 1: Understand the Length of the Minute Hand
The minute hand of the watch is given to be 1.5 cm long. This length represents the radius (r) of the circular path traced by the tip of the minute hand.

### Step 2: Calculate the Total Angle in Radians
The minute hand completes one full revolution (360 degrees) in 60 minutes. Therefore, in 40 minutes, the angle (θ) covered by the minute hand can be calculated as follows:

\[ \text{Angle in degrees} = \left(\frac{40 \text{ minutes}}{60 \text{ minutes}}\right) \times 360 \text{ degrees} = 240 \text{ degrees} \]

To convert degrees to radians, we use the conversion factor \( \frac{\pi}{180} \):

\[ \text{Angle in radians} = 240 \times \frac{\pi}{180} = \frac{240\pi}{180} = \frac{4\pi}{3} \text{ radians} \]

### Step 3: Calculate the Distance Traveled by the Tip
The distance (s) traveled by the tip of the minute hand can be calculated using the formula:

\[ s = r \times \theta \]

Where:
- \( r = 1.5 \) cm (length of the minute hand)
- \( \theta = \frac{4\pi}{3} \) radians

Substituting the values:

\[ s = 1.5 \times \frac{4\pi}{3} \]

Now substituting \( \pi = 3.14 \):

\[ s = 1.5 \times \frac{4 \times 3.14}{3} = 1.5 \times \frac{12.56}{3} = 1.5 \times 4.18667 \approx 6.28001 \text{ cm} \]

### Final Answer
The tip of the minute hand moves approximately **6.28 cm** in 40 minutes.

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