A wheel makes 4000 revolutions in moving a distance of 44 km. Find the radius of the wheel.

Options

A. 15 m
B. 27 m
C. 25 m
D. 28 m

Answer

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

### Step 1: Calculate the distance covered in one revolution.
The wheel makes 4000 revolutions to cover a distance of 44 kilometers. To find the distance covered in one revolution, we divide the total distance by the number of revolutions.

\[ \text{Distance in one revolution} = \frac{\text{Total Distance}}{\text{Number of Revolutions}} = \frac{44 \text{ km}}{4000} \]

### Step 2: Convert kilometers to meters.
Since we want the radius in meters, we need to convert kilometers to meters. We know that 1 kilometer = 1000 meters.

\[ \text{Distance in one revolution} = \frac{44 \times 1000 \text{ m}}{4000} = \frac{44000 \text{ m}}{4000} \]

### Step 3: Simplify the calculation.
Now, we simplify the fraction:

\[ \text{Distance in one revolution} = \frac{44000}{4000} = 11 \text{ m} \]

### Step 4: Use the circumference formula to find the radius.
The distance covered in one revolution is equal to the circumference of the wheel. The formula for the circumference \(C\) of a circle is given by:

\[ C = 2\pi r \]

Setting the circumference equal to the distance covered in one revolution:

\[ 2\pi r = 11 \]

### Step 5: Solve for the radius \(r\).
To find the radius, we rearrange the equation:

\[ r = \frac{11}{2\pi} \]

### Step 6: Calculate the value of \(r\).
Using the value of \(\pi \approx 3.14\):

\[ r = \frac{11}{2 \times 3.14} \approx \frac{11}{6.28} \approx 1.75 \text{ m} \]

### Final Answer:
The radius of the wheel is approximately **1.75 meters**.

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