A bicycle wheel makes 5000 revolutions in moving 11km. Then the radius of the wheel (in cm) is

Options

A. 70
B. 35
C. 17.5
D. 140

Answer

To find the radius of the bicycle wheel, we can follow these steps:

### Step 1: Understand the relationship between revolutions and distance
The distance covered by the bicycle wheel in one revolution is equal to the circumference of the wheel. If the wheel makes 5000 revolutions to cover a total distance of 11 km, we can first convert this distance into meters for easier calculations.

### Step 2: Convert kilometers to meters
1 kilometer is equal to 1000 meters. Therefore, 11 kilometers is:
\[ 11 \text{ km} = 11 \times 1000 = 11000 \text{ meters} \]

### Step 3: Calculate the distance covered in one revolution
The distance covered in one revolution can be calculated by dividing the total distance by the number of revolutions:
\[ \text{Distance per revolution} = \frac{\text{Total distance}}{\text{Number of revolutions}} \]
Substituting the values:
\[ \text{Distance per revolution} = \frac{11000 \text{ meters}}{5000} = \frac{11}{5} \text{ meters} \]

### Step 4: Convert the distance from meters to centimeters
Since we need to find the radius in centimeters, we convert the distance per revolution from meters to centimeters. There are 100 centimeters in a meter, so:
\[ \text{Distance per revolution in cm} = \frac{11}{5} \times 100 = 220 \text{ cm} \]

### Step 5: Use the circumference formula to find the radius
The circumference \( C \) of a circle is given by the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius. We have found that the circumference is 220 cm, so we set up the equation:
\[ 2 \pi r = 220 \]

### Step 6: Solve for the radius \( r \)
To isolate \( r \), we can rearrange the equation:
\[ r = \frac{220}{2 \pi} \]
Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{220}{2 \times \frac{22}{7}} = \frac{220 \times 7}{44} \]
Simplifying:
\[ r = \frac{1540}{44} = 35 \text{ cm} \]

### Final Answer
The radius of the bicycle wheel is:
\[ \boxed{35 \text{ cm}} \]