The radius of a wheel is 0.25m. How many revolutions will it take in covering 11 km?

Options

A. 2800
B. 4000
C. 5500
D. 7000

Explanation

To solve the problem step by step, we will determine how many revolutions a wheel with a radius of 0.25 meters will take to cover a distance of 11 kilometers.

### Step 1: Calculate the circumference of the wheel
The circumference \( C \) of a circle (or wheel in this case) is given by the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius. Here, the radius \( r = 0.25 \) meters.

Substituting the value of \( r \):
\[ C = 2 \times \pi \times 0.25 \]
Using \( \pi \approx \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 0.25 \]
Calculating this:
\[ C = 2 \times \frac{22 \times 0.25}{7} = 2 \times \frac{5.5}{7} = \frac{11}{7} \text{ meters} \]

### Step 2: Convert the distance from kilometers to meters
The total distance to be covered is 11 kilometers. We convert this distance to meters:
\[ 11 \text{ km} = 11 \times 1000 \text{ m} = 11000 \text{ m} \]

### Step 3: Calculate the number of revolutions
The number of revolutions \( N \) can be calculated using the formula:
\[ N = \frac{\text{Total Distance}}{\text{Circumference}} \]
Substituting the values we have:
\[ N = \frac{11000}{\frac{11}{7}} = 11000 \times \frac{7}{11} \]
The \( 11 \) in the numerator and denominator cancels out:
\[ N = 1000 \times 7 = 7000 \]

### Final Answer
The number of revolutions the wheel will take to cover 11 kilometers is **7000**.

---