A wheel completes 2000 revolutions to cover the 9.5 km. distance. then the diameter of the wheel is

Options

A. `1.5m`
B. `1.5 cm`
C. `7.5 cm`
D. `7.5 m`

Answer

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

### Step 1: Convert the distance from kilometers to meters
The distance covered by the wheel is given as 9.5 km. We need to convert this distance into meters for consistency in units.

\[ \text{Distance} = 9.5 \, \text{km} = 9.5 \times 1000 \, \text{m} = 9500 \, \text{m} \]

### Step 2: Understand the relationship between distance, revolutions, and circumference
The distance covered in one complete revolution of the wheel is equal to the circumference of the wheel. The circumference \( C \) can be expressed in terms of the radius \( r \) as:

\[ C = 2 \pi r \]

Since the wheel completes 2000 revolutions, the total distance \( s \) covered can be expressed as:

\[ s = n \times C = n \times (2 \pi r) \]

Where \( n \) is the number of revolutions (2000 in this case).

### Step 3: Substitute the known values into the equation
We know that the total distance \( s \) is 9500 m and the number of revolutions \( n \) is 2000. Therefore, we can write:

\[ 9500 = 2000 \times (2 \pi r) \]

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

\[ 2 \pi r = \frac{9500}{2000} \]

Calculating the right side:

\[ 2 \pi r = 4.75 \]

Now, divide both sides by \( 2 \pi \):

\[ r = \frac{4.75}{2 \pi} \]

### Step 5: Calculate the diameter \( d \)
The diameter \( d \) is twice the radius:

\[ d = 2r = 2 \times \frac{4.75}{2 \pi} = \frac{4.75}{\pi} \]

### Step 6: Compute the value of \( d \)
Now, we can substitute the value of \( \pi \) (approximately 3.14) to find \( d \):

\[ d \approx \frac{4.75}{3.14} \approx 1.51 \, \text{m} \]

### Final Answer
Thus, the diameter of the wheel is approximately:

\[ \text{Diameter} \approx 1.51 \, \text{m} \]