The wheel of a motor car make 1000 revolutions in moving 440 m. The diameter (in metre) of the wheel is

Options

A. `0.44`
B. `0.14`
C. `0.24`
D. `0.34`

Answer

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

### Step 1: Calculate the distance covered in one revolution
The total distance covered by the wheel is 440 meters, and the wheel makes 1000 revolutions.

To find the distance covered in one revolution, we can use the formula:
\[ \text{Distance per revolution} = \frac{\text{Total distance}}{\text{Number of revolutions}} = \frac{440 \text{ m}}{1000} = 0.44 \text{ m} \]

### Step 2: Relate the distance per revolution to the circumference
The distance covered in one revolution is equal to the circumference of the wheel. Therefore:
\[ \text{Circumference} = 0.44 \text{ m} \]

### Step 3: Use the circumference 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 can rearrange this formula to solve for \(r\):
\[ r = \frac{C}{2\pi} = \frac{0.44}{2\pi} \]

Using \(\pi \approx \frac{22}{7}\), we can substitute:
\[ r = \frac{0.44}{2 \times \frac{22}{7}} = \frac{0.44 \times 7}{44} = \frac{3.08}{44} = \frac{7}{100} \text{ m} \]

### Step 4: Calculate the diameter
The diameter \(d\) of the wheel is twice the radius:
\[ d = 2r = 2 \times \frac{7}{100} = \frac{14}{100} = 0.14 \text{ m} \]

### Final Answer
The diameter of the wheel is \(0.14\) meters.

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