The radii of the wheel of a car is 28 cm. Find the number of rotations made by the wheel in order to cover a distance of 4.4 km ?

Answer

To solve the problem of finding the number of rotations made by a car wheel with a radius of 28 cm to cover a distance of 4.4 km, we can follow these steps:

### Step 1: Calculate the Circumference of the Wheel
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

Given:
- Radius \( r = 28 \) cm

Substituting the value of \( r \):
\[ C = 2 \times \pi \times 28 \]
Using \( \pi \approx \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 28 \]
Calculating:
\[ C = \frac{44 \times 28}{7} = \frac{1232}{7} = 176 \text{ cm} \]

### Step 2: Convert Distance from Kilometers to Centimeters
The distance to be covered is given as 4.4 km. We need to convert this distance into centimeters.

1 km = 1000 meters
1 meter = 100 cm

Thus,
\[ 1 \text{ km} = 1000 \times 100 = 100000 \text{ cm} \]
Now, converting 4.4 km:
\[ 4.4 \text{ km} = 4.4 \times 100000 \text{ cm} = 440000 \text{ cm} \]

### Step 3: Calculate the Number of Rotations
The number of rotations \( N \) made by the wheel can be calculated using the formula:
\[ N = \frac{\text{Distance}}{\text{Circumference}} \]

Substituting the values we have:
\[ N = \frac{440000 \text{ cm}}{176 \text{ cm}} \]
Calculating:
\[ N = 2500 \]

### Final Answer
The number of rotations made by the wheel is **2500**.

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