A bicycle wheel makes 5000 revolutions in moving 11 km. Find the circumference and the diameter of the wheel.

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Convert kilometers to meters
The first step is to convert the distance traveled from kilometers to meters.

Given:
- Distance = 11 km

We know that:
1 km = 1000 meters

So,
\[ \text{Distance in meters} = 11 \times 1000 = 11000 \text{ meters} \]

### Step 2: Calculate the distance covered in one revolution
Next, we need to find out how far the bicycle travels in one revolution of the wheel.

Given:
- Total revolutions = 5000

Using the formula:
\[ \text{Distance per revolution} = \frac{\text{Total distance}}{\text{Total revolutions}} \]

Substituting the values:
\[ \text{Distance per revolution} = \frac{11000 \text{ meters}}{5000} = 2.2 \text{ meters} \]

### Step 3: Relate distance per revolution to circumference
The distance covered in one revolution of the wheel is equal to the circumference of the wheel.

So, we have:
\[ \text{Circumference} = 2.2 \text{ meters} \]

### Step 4: Calculate the diameter of the wheel
The circumference (C) of a circle is related to its diameter (D) by the formula:
\[ C = \pi D \]

We can rearrange this to find the diameter:
\[ D = \frac{C}{\pi} \]

Using \( \pi \approx \frac{22}{7} \):
\[ D = \frac{2.2}{\frac{22}{7}} \]

To simplify:
\[ D = 2.2 \times \frac{7}{22} \]
\[ D = \frac{2.2 \times 7}{22} \]
\[ D = \frac{15.4}{22} \]
\[ D = 0.7 \text{ meters} \]

### Final Answers
- Circumference of the wheel = 2.2 meters
- Diameter of the wheel = 0.7 meters

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