If the radius of a wheel is 14 cm, find the distance covered in 150 revolutions.

Options

A. `15,200 cm`
B. `13,200 cm`
C. `14,200 cm`
D. `16,200 cm`

Answer

To find the distance covered by a wheel in 150 revolutions when the radius is given as 14 cm, we can follow these steps:

### Step 1: Calculate the Circumference of the Wheel
The formula for the circumference \( C \) of a circle (or wheel) is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the wheel.

Given:
- Radius \( r = 14 \) cm

Substituting the value of \( r \):
\[ C = 2 \pi \times 14 \]

### Step 2: Substitute the Value of \( \pi \)
We can use \( \pi \approx \frac{22}{7} \) for our calculations:
\[ C = 2 \times \frac{22}{7} \times 14 \]

### Step 3: Simplify the Calculation
Now, let's simplify the expression:
\[ C = 2 \times \frac{22 \times 14}{7} \]
Calculating \( 22 \times 14 \):
\[ 22 \times 14 = 308 \]
Now substituting back:
\[ C = 2 \times \frac{308}{7} \]
\[ C = \frac{616}{7} \text{ cm} \]

### Step 4: Calculate the Distance for 150 Revolutions
The distance covered in 150 revolutions is given by:
\[ \text{Distance} = 150 \times C \]
Substituting the value of \( C \):
\[ \text{Distance} = 150 \times \frac{616}{7} \]

### Step 5: Perform the Multiplication
Calculating the distance:
\[ \text{Distance} = \frac{150 \times 616}{7} \]
Calculating \( 150 \times 616 \):
\[ 150 \times 616 = 92400 \]
So,
\[ \text{Distance} = \frac{92400}{7} \]

### Step 6: Divide to Find the Final Distance
Now, dividing:
\[ \text{Distance} = 13200 \text{ cm} \]

### Step 7: Convert to Meters
Since 100 cm = 1 m, we can convert the distance into meters:
\[ \text{Distance in meters} = \frac{13200}{100} = 132 \text{ m} \]

### Final Answer
The distance covered in 150 revolutions is **13200 cm** or **132 m**.

---