The number of revolutions made by a circular wheel of radius `0.7` m in rolling a distance of `176` m is :

Options

A. `22`
B. `24`
C. `75`
D. `40`

Answer

To find the number of revolutions made by a circular wheel of radius 0.7 m in rolling a distance of 176 m, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to calculate how many times the wheel revolves as it rolls a distance of 176 meters.

2. **Formula for Circumference**: The distance covered in one revolution of the wheel is equal to its circumference. The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

3. **Substituting the Radius**: Given that the radius \( r = 0.7 \) m, we can substitute this value into the circumference formula:
\[ C = 2 \pi (0.7) = 1.4 \pi \]

4. **Using Approximation for Pi**: We can use \( \pi \approx \frac{22}{7} \) for calculation:
\[ C = 1.4 \times \frac{22}{7} \]

5. **Calculating the Circumference**:
\[ C = \frac{1.4 \times 22}{7} = \frac{30.8}{7} \approx 4.4 \text{ m} \]

6. **Calculating the Number of Revolutions**: The number of revolutions \( N \) can be calculated by dividing the total distance rolled by the circumference:
\[ N = \frac{\text{Total Distance}}{\text{Circumference}} = \frac{176}{4.4} \]

7. **Performing the Division**:
\[ N = 40 \]

### Final Answer:
The number of revolutions made by the circular wheel is **40**.

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