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 circumference (C) of a circle (or wheel) is given by the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius.

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

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

### Step 2: Perform the Calculation
Calculating the circumference:
\[ C = 2 \times \frac{22}{7} \times 28 = \frac{44 \times 28}{7} \]
\[ C = \frac{1232}{7} \]
\[ C = 176 \text{ cm} \]

### Step 3: Convert Circumference to Meters
Since the distance to be covered is in meters, we need to convert the circumference from centimeters to meters:
\[ C = 176 \text{ cm} = \frac{176}{100} \text{ m} = 1.76 \text{ m} \]

### Step 4: Calculate the Number of Rotations
The number of rotations (N) required to cover a distance (D) is given by:
\[ N = \frac{D}{C} \]

Given:
- Distance \( D = 352 \) m

Substituting the values:
\[ N = \frac{352}{1.76} \]

### Step 5: Perform the Calculation
Calculating the number of rotations:
\[ N = 200 \]

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

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