The radius of the wheel of a car is 35 cm. How many revolutions will it make to travel 33 km?

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Find the Circumference of the Wheel
The circumference \( C \) of a circle (which represents the distance the wheel covers in one revolution) is calculated using the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius of the wheel.

Given:
- Radius \( r = 35 \) cm
- Using \( \pi \approx \frac{22}{7} \)

Substituting the values:
\[ C = 2 \times \frac{22}{7} \times 35 \]

### Step 2: Calculate the Circumference
Calculating the above expression:
\[ C = 2 \times \frac{22}{7} \times 35 = 2 \times \frac{770}{7} = \frac{1540}{7} \approx 220 \text{ cm} \]

### Step 3: Convert Distance from Kilometers to Centimeters
The total distance to be traveled is given as 33 km. We need to convert this distance into centimeters:
\[ 1 \text{ km} = 1000 \text{ m} = 100000 \text{ cm} \]
Thus,
\[ 33 \text{ km} = 33 \times 100000 = 3300000 \text{ cm} \]

### Step 4: Calculate the Number of Revolutions
To find the number of revolutions \( N \) the wheel makes to cover the total distance, we divide the total distance by the circumference:
\[ N = \frac{\text{Total Distance}}{\text{Circumference}} = \frac{3300000 \text{ cm}}{220 \text{ cm}} \]

### Step 5: Perform the Division
Calculating the number of revolutions:
\[ N = \frac{3300000}{220} = 15000 \]

### Final Answer
The wheel will make **15,000 revolutions** to travel 33 km.

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