How many times a wheel of radius `28 cm` must rotate to go `352 m`? (Take `pi = 22/7`)

Options

A. `100`
B. `300`
C. `200`
D. `400`

Explanation

To find out how many times a wheel of radius 28 cm must rotate to cover a distance of 352 m, 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 wheel.

Given:
- Radius \( r = 28 \) cm
- \( \pi = \frac{22}{7} \)

Substituting the values into the formula:
\[ C = 2 \times \frac{22}{7} \times 28 \]

### Step 2: Simplify the Calculation
Calculating the circumference:
\[ C = 2 \times \frac{22 \times 28}{7} \]
First, calculate \( 22 \times 28 \):
\[ 22 \times 28 = 616 \]
Now substitute back:
\[ C = 2 \times \frac{616}{7} = \frac{1232}{7} \text{ cm} \]
Calculating \( \frac{1232}{7} \):
\[ C = 176 \text{ cm} \]

### Step 3: Convert Distance from Meters to Centimeters
Since the distance to be covered is given in meters, we need to convert it to centimeters:
\[ 352 \text{ m} = 352 \times 100 \text{ cm} = 35200 \text{ cm} \]

### Step 4: Calculate the Number of Rotations
To find the number of rotations \( N \), we use the formula:
\[ N = \frac{\text{Total Distance}}{\text{Circumference}} \]
Substituting the values we have:
\[ N = \frac{35200 \text{ cm}}{176 \text{ cm}} \]

### Step 5: Perform the Division
Calculating \( N \):
\[ N = 200 \]

### Final Answer
The wheel must rotate **200 times** to cover a distance of 352 m.

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