The wheel of a cycle covers 660 metres by making 500 revolutions. What is the diameter of the wheel (in cm)?

Options

A. 42
B. 21
C. 30
D. 60

Answer

To find the diameter of the wheel of a cycle that covers 660 meters in 500 revolutions, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between distance, revolutions, and diameter**:
- The distance covered in one revolution of the wheel is equal to the circumference of the wheel, which can be calculated using the formula:
\[ \text{Circumference} = 2 \pi r \]
- Here, \( r \) is the radius of the wheel.

2. **Calculate the total distance covered in terms of the radius**:
- If the wheel makes 500 revolutions, the total distance covered can be expressed as:
\[ \text{Total Distance} = 500 \times \text{Circumference} = 500 \times 2 \pi r \]

3. **Set up the equation**:
- We know the total distance covered is 660 meters, so we can set up the equation:
\[ 500 \times 2 \pi r = 660 \]

4. **Simplify the equation**:
- Divide both sides of the equation by 500:
\[ 2 \pi r = \frac{660}{500} \]
- This simplifies to:
\[ 2 \pi r = \frac{66}{50} \]

5. **Express the diameter in terms of the radius**:
- The diameter \( d \) is related to the radius by the formula:
\[ d = 2r \]
- We can substitute \( r \) in terms of \( d \):
\[ 2 \pi \left(\frac{d}{2}\right) = \frac{66}{50} \]
- This simplifies to:
\[ \pi d = \frac{66}{50} \]

6. **Substitute the value of \( \pi \)**:
- Using \( \pi \approx \frac{22}{7} \):
\[ \frac{22}{7} d = \frac{66}{50} \]

7. **Solve for \( d \)**:
- Multiply both sides by 7:
\[ 22d = \frac{66 \times 7}{50} \]
- Simplify the right side:
\[ 22d = \frac{462}{50} \]
- Divide both sides by 22:
\[ d = \frac{462}{50 \times 22} \]
- Simplifying further:
\[ d = \frac{462}{1100} = \frac{21}{50} \text{ meters} \]

8. **Convert meters to centimeters**:
- Since 1 meter = 100 centimeters, we convert the diameter:
\[ d = \frac{21}{50} \times 100 = 42 \text{ cm} \]

### Final Answer:
The diameter of the wheel is **42 cm**.