The radius of a bicycle wheel is 14 cm . The distance covered by the wheel after making 50 complete rotation is

Options

A. 88 cm
B. 2200 cm
C. 440 cm
D. 4400 cm

Answer

To find the distance covered by a bicycle wheel after making 50 complete rotations, we can follow these steps:

### Step 1: Identify the radius of the wheel
The radius \( r \) of the bicycle wheel is given as 14 cm.

### Step 2: Calculate the circumference of the wheel
The distance covered in one complete rotation of the wheel is equal to the circumference of the circle. The formula for the circumference \( C \) is:
\[ C = 2 \pi r \]
Substituting the value of \( r \):
\[ C = 2 \times \pi \times 14 \]

### Step 3: Substitute the value of \( \pi \)
For calculations, we can use \( \pi \approx \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 14 \]

### Step 4: Simplify the expression
Calculating this step-by-step:
1. First, calculate \( 2 \times 14 = 28 \).
2. Now, substitute this back into the equation:
\[ C = \frac{22}{7} \times 28 \]
3. Simplifying \( \frac{28}{7} = 4 \):
\[ C = 22 \times 4 = 88 \text{ cm} \]

### Step 5: Calculate the distance covered in 50 rotations
Now that we have the circumference for one rotation, we can find the distance covered in 50 rotations:
\[ \text{Distance} = 50 \times C = 50 \times 88 \]

### Step 6: Perform the multiplication
Calculating this:
\[ 50 \times 88 = 4400 \text{ cm} \]

### Final Answer
The distance covered by the wheel after making 50 complete rotations is **4400 cm**.

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