The diameter of the wheel of a car is 77 cm. How many revolutions will it make to travel121 km? 

Answer

To solve the problem of how many revolutions a car wheel will make to travel 121 km, given that the diameter of the wheel is 77 cm, we can follow these steps:

### Step 1: Calculate the Radius of the Wheel
The radius (r) is half of the diameter.
- **Formula**: \( r = \frac{d}{2} \)
- **Calculation**: \( r = \frac{77 \text{ cm}}{2} = 38.5 \text{ cm} \)

### Step 2: Calculate the Circumference of the Wheel
The circumference (C) of the wheel is the distance covered in one complete revolution.
- **Formula**: \( C = 2\pi r \)
- **Using \( \pi \approx \frac{22}{7} \)**:
- \( C = 2 \times \frac{22}{7} \times 38.5 \)
- \( C = \frac{44 \times 38.5}{7} \)
- \( C = \frac{1694}{7} \)
- \( C \approx 242 \text{ cm} \)

### Step 3: Convert the Distance from Kilometers to Centimeters
We need to convert the distance of 121 km into centimeters.
- **Conversion**: \( 1 \text{ km} = 100,000 \text{ cm} \)
- **Calculation**:
- \( 121 \text{ km} = 121 \times 100,000 \text{ cm} = 12,100,000 \text{ cm} \)

### Step 4: Calculate the Number of Revolutions
To find the number of revolutions (N), we divide the total distance traveled by the circumference of the wheel.
- **Formula**: \( N = \frac{\text{Total Distance}}{\text{Circumference}} \)
- **Calculation**:
- \( N = \frac{12,100,000 \text{ cm}}{242 \text{ cm}} \)
- \( N \approx 50,000 \)

### Final Answer
The wheel will make approximately **50,000 revolutions** to travel 121 km.

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