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, we need to find the number of revolutions a wheel makes when it travels a distance of 2.904 km, given that the radius of the wheel is 77 cm.

### Step-by-Step Solution:

1. **Find the Circumference of the Wheel:**
The circumference (C) of a circle (which represents the distance covered in one revolution) can be calculated using the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius of the wheel. Given \( r = 77 \) cm, we can substitute this value into the formula.

\[ C = 2 \times \frac{22}{7} \times 77 \]
\[ C = \frac{44}{7} \times 77 \]
\[ C = \frac{44 \times 77}{7} \]
\[ C = \frac{3388}{7} = 484 \text{ cm} \]

2. **Convert the Distance to the Same Unit:**
The distance traveled is given as 2.904 km. We need to convert this distance into centimeters to match the unit of the circumference.
\[ 2.904 \text{ km} = 2.904 \times 1000 \text{ m} = 2904 \text{ m} \]
\[ 2904 \text{ m} = 2904 \times 100 \text{ cm} = 290400 \text{ cm} \]

3. **Calculate the Number of Revolutions:**
The number of revolutions (N) can be calculated using the formula:
\[ N = \frac{\text{Total Distance}}{\text{Circumference}} \]
Substituting the values we have:
\[ N = \frac{290400 \text{ cm}}{484 \text{ cm}} \]
\[ N = 600 \]

### Final Answer:
The number of revolutions the wheel will make in traveling a distance of 2.904 km is **600 revolutions**.

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