The radius of a wheel is 77 cm, find the number of revolutions it will make in travelling a distance of 2.904 km

Answer

To solve the problem of finding the number of revolutions a wheel makes when traveling a distance of 2.904 km with a radius of 77 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the radius of the wheel**:
The radius of the wheel is given as 77 cm.

2. **Calculate the circumference of the wheel**:
The distance covered in one revolution of the wheel is equal to its circumference. The formula for the circumference \( C \) of a circle is:
\[ C = 2 \pi r \]
Substituting the value of \( r \):
\[ C = 2 \times \frac{22}{7} \times 77 \]
Simplifying this:
\[ C = 2 \times \frac{22 \times 77}{7} = 2 \times \frac{1694}{7} = \frac{3388}{7} = 484 \text{ cm} \]

3. **Convert the total distance from kilometers to centimeters**:
The total distance traveled is given as 2.904 km. To convert this to centimeters:
\[ 2.904 \text{ km} = 2.904 \times 1000 \text{ m} = 2904 \text{ m} \]
Now converting meters to centimeters:
\[ 2904 \text{ m} = 2904 \times 100 \text{ cm} = 290400 \text{ cm} \]

4. **Calculate the number of revolutions**:
The number of revolutions \( N \) can be calculated by dividing the total distance traveled by the circumference of the wheel:
\[ N = \frac{\text{Total Distance}}{\text{Circumference}} = \frac{290400 \text{ cm}}{484 \text{ cm}} \]
Performing the division:
\[ N = 600 \]

5. **Final Answer**:
Therefore, the number of revolutions the wheel makes is **600**.