The length of minute hand of a wall clock is 12 cm. find the distance covered by the tip of the minutes hand in 25 minutes.

Options

A. `(220)/(7)`cm
B. `(110)/(7)`cm
C. `(120)/(7)`cm
D. `(240)/(7)`cm

Explanation

To find the distance covered by the tip of the minute hand of a clock in 25 minutes, we can follow these steps:

### Step 1: Find the Circumference of the Circle
The minute hand moves in a circular path, and the distance covered by the tip of the minute hand can be determined by calculating the circumference of the circle. The formula for the circumference (C) of a circle is:

\[ C = 2 \pi r \]

Where \( r \) is the radius of the circle. Here, the length of the minute hand is given as 12 cm, which is the radius.

\[ C = 2 \times \pi \times 12 \]

Using \( \pi \approx \frac{22}{7} \):

\[ C = 2 \times \frac{22}{7} \times 12 = \frac{528}{7} \approx 75.43 \text{ cm} \]

### Step 2: Calculate the Angle Covered in 25 Minutes
The minute hand completes a full circle (360 degrees) in 60 minutes. To find the angle covered in 25 minutes, we can set up a proportion:

\[ \text{Angle covered} = \frac{360 \text{ degrees}}{60 \text{ minutes}} \times 25 \text{ minutes} \]

Calculating this gives:

\[ \text{Angle covered} = 6 \times 25 = 150 \text{ degrees} \]

### Step 3: Calculate the Distance Covered in 150 Degrees
Now, we need to find the distance covered by the minute hand for the 150 degrees it has moved. First, we find the distance covered in 1 degree:

\[ \text{Distance per degree} = \frac{\text{Circumference}}{360} \]

Substituting the circumference we calculated:

\[ \text{Distance per degree} = \frac{75.43}{360} \approx 0.209 \text{ cm} \]

Now, we can find the distance covered in 150 degrees:

\[ \text{Distance covered in 150 degrees} = 150 \times 0.209 \approx 31.35 \text{ cm} \]

### Final Answer
The distance covered by the tip of the minute hand in 25 minutes is approximately **31.35 cm**.

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