The length of the minutes hand of a wall clock is 36 cm. Find the distance covered by its tip in 35 minutes.

Answer

To find the distance covered by the tip of the minute hand of a wall clock in 35 minutes, we can follow these steps:

### Step 1: Understand the problem
The minute hand of the clock acts like the radius of a circle. The length of the minute hand is given as 36 cm, which means the radius (r) of the circle is 36 cm.

### Step 2: Find the angle covered by the minute hand in 35 minutes
The minute hand completes one full rotation (360 degrees) in 60 minutes. Therefore, in 1 minute, it covers:
\[ \text{Angle per minute} = \frac{360 \text{ degrees}}{60 \text{ minutes}} = 6 \text{ degrees} \]
In 35 minutes, the angle covered by the minute hand is:
\[ \text{Angle in 35 minutes} = 6 \text{ degrees/minute} \times 35 \text{ minutes} = 210 \text{ degrees} \]

### Step 3: Convert the angle to radians
To use the formula for the arc length, we need to convert degrees to radians. The conversion factor is:
\[ \text{Radians} = \text{Degrees} \times \frac{\pi}{180} \]
Thus, the angle in radians is:
\[ \theta = 210 \times \frac{\pi}{180} = \frac{210\pi}{180} = \frac{7\pi}{6} \text{ radians} \]

### Step 4: Use the arc length formula
The formula for the arc length (s) is given by:
\[ s = r \times \theta \]
Where:
- \( r \) is the radius (36 cm)
- \( \theta \) is the angle in radians

Substituting the values:
\[ s = 36 \times \frac{7\pi}{6} \]
\[ s = 36 \times \frac{7 \times 3.14}{6} \quad (\text{using } \pi \approx 3.14) \]
\[ s = 36 \times \frac{21.98}{6} = 36 \times 3.6633 \approx 132 \text{ cm} \]

### Final Answer
The distance covered by the tip of the minute hand in 35 minutes is approximately **132 cm**.

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