The number of revolutions a wheel of diameter 40 cm makes in travelling a distance of 176 m is `(pi = 22/7)`

Options

A. 140
B. 150
C. 160
D. 166

Answer

To solve the problem of finding the number of revolutions a wheel of diameter 40 cm makes in traveling a distance of 176 m, we will follow these steps:

### Step-by-Step Solution:

1. **Convert Distance from Meters to Centimeters:**
- The total distance traveled is given as 176 meters.
- We know that 1 meter = 100 centimeters.
- Therefore, to convert 176 meters to centimeters:
\[ \text{Total Distance (D)} = 176 \times 100 = 17600 \text{ cm} \]

2. **Find the Radius of the Wheel:**
- The diameter of the wheel is given as 40 cm.
- The radius (r) is half of the diameter:
\[ r = \frac{\text{Diameter}}{2} = \frac{40}{2} = 20 \text{ cm} \]

3. **Calculate the Circumference of the Wheel:**
- The formula for the circumference (C) of a circle is:
\[ C = 2 \pi r \]
- Substituting the values (using \(\pi = \frac{22}{7}\)):
\[ C = 2 \times \frac{22}{7} \times 20 \]
- Simplifying this:
\[ C = \frac{44}{7} \times 20 = \frac{880}{7} \text{ cm} \]

4. **Calculate the Number of Revolutions:**
- The number of revolutions is given by the formula:
\[ \text{Number of Revolutions} = \frac{\text{Total Distance}}{\text{Circumference}} \]
- Substituting the values we have:
\[ \text{Number of Revolutions} = \frac{17600}{\frac{880}{7}} \]
- This can be simplified by multiplying by the reciprocal:
\[ = 17600 \times \frac{7}{880} \]
- Now, simplify \(17600 \div 880\):
\[ 17600 \div 880 = 20 \quad \text{(since } 17600 = 20 \times 880\text{)} \]
- Therefore:
\[ \text{Number of Revolutions} = 20 \times 7 = 140 \]

5. **Final Answer:**
- The number of revolutions the wheel makes is **140**.