A wheel covers a distance of 60 km in 4000 rotations. The radius of wheel is

Options

A. 8.25 metre
B. 8 metre
C. 2.38 metre
D. 4.68 metre

Answer

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

### Step 1: Calculate the distance covered in one rotation of the wheel.
The total distance covered by the wheel is given as 60 km in 4000 rotations. To find the distance covered in one rotation, we can use the formula:

\[ \text{Distance per rotation} = \frac{\text{Total distance}}{\text{Number of rotations}} \]

Substituting the values:

\[ \text{Distance per rotation} = \frac{60 \text{ km}}{4000} = 0.015 \text{ km} \]

### Step 2: Convert the distance per rotation to meters.
Since 1 km = 1000 meters, we convert the distance per rotation from kilometers to meters:

\[ 0.015 \text{ km} = 0.015 \times 1000 \text{ m} = 15 \text{ m} \]

### Step 3: Relate the distance per rotation to the circumference of the wheel.
The distance covered in one rotation of the wheel is equal to the circumference of the wheel. The formula for the circumference \(C\) of a circle is given by:

\[ C = 2\pi r \]

where \(r\) is the radius of the wheel. Setting the circumference equal to the distance per rotation, we have:

\[ 2\pi r = 15 \text{ m} \]

### Step 4: Solve for the radius \(r\).
To find the radius, we rearrange the equation:

\[ r = \frac{15}{2\pi} \]

Now, substituting the value of \(\pi \approx 3.14\):

\[ r = \frac{15}{2 \times 3.14} \approx \frac{15}{6.28} \approx 2.39 \text{ m} \]

### Conclusion
The radius of the wheel is approximately \(2.39\) meters.

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