The minute hand of a clock is 15 cm long. How far does the tip of the hand move during 40 minutes ? (Take `pi=3.14` )

Answer

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

### Step 1: Identify the length of the minute hand
The length of the minute hand is given as 15 cm.

### Step 2: Determine the angle moved in 40 minutes
In a clock, the minute hand completes a full circle (360 degrees) in 60 minutes. Therefore, we can calculate the angle moved in 40 minutes using the following proportion:

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

Calculating this gives:

\[ \text{Angle moved} = \frac{360}{60} \times 40 = 6 \times 40 = 240 \text{ degrees} \]

### Step 3: Convert the angle from degrees to radians
To find the arc length, we need to convert the angle from degrees to radians. The conversion formula is:

\[ \text{Radians} = \text{Degrees} \times \frac{\pi}{180} \]

Substituting the angle we found:

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

### Step 4: Calculate the arc length
The arc length (distance traveled by the tip of the minute hand) can be calculated using the formula:

\[ \text{Arc Length} = \text{Angle in radians} \times \text{Radius} \]

Here, the radius is the length of the minute hand (15 cm):

\[ \text{Arc Length} = \frac{4\pi}{3} \times 15 \]

Calculating this gives:

\[ \text{Arc Length} = 20\pi \]

### Step 5: Substitute the value of \(\pi\)
We are given that \(\pi = 3.14\). Substituting this value into the arc length formula:

\[ \text{Arc Length} = 20 \times 3.14 = 62.8 \text{ cm} \]

### Final Answer
The distance that the tip of the minute hand moves during 40 minutes is **62.8 cm**.

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