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

Options

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

Explanation

To find the diameter of the wheel that completes 2000 revolutions to cover a distance of 9.5 km, we can follow these steps:

### Step 1: Understand the relationship between revolutions and distance
When a wheel makes one complete revolution, it covers a distance equal to the circumference of the wheel. The circumference \( C \) of a circle (or wheel) is given by the formula:
\[ C = \pi D \]
where \( D \) is the diameter of the wheel.

### Step 2: Calculate the total distance covered in terms of diameter
If the wheel completes 2000 revolutions, the total distance \( S \) covered can be expressed as:
\[ S = \text{Number of revolutions} \times \text{Circumference} \]
Substituting the circumference, we have:
\[ S = 2000 \times \pi D \]

### Step 3: Set up the equation with the given distance
We know from the problem that the total distance \( S \) is 9.5 km. We need to convert this distance into meters for consistency in units:
\[ 9.5 \text{ km} = 9.5 \times 1000 \text{ m} = 9500 \text{ m} \]
Now we can set up the equation:
\[ 2000 \pi D = 9500 \]

### Step 4: Solve for the diameter \( D \)
To find \( D \), we rearrange the equation:
\[ D = \frac{9500}{2000 \pi} \]
Now substituting the value of \( \pi \) (approximately \( 3.14 \)):
\[ D = \frac{9500}{2000 \times 3.14} \]
Calculating the denominator:
\[ 2000 \times 3.14 = 6280 \]
Now substituting back:
\[ D = \frac{9500}{6280} \]
Calculating this gives:
\[ D \approx 1.51 \text{ m} \]

### Conclusion
The diameter of the wheel is approximately \( 1.51 \) meters.

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