A wheel of a car rotated 1000 times in travelling a distance of 1.76 km . Find the radius of the wheel . (Take `pi=(22)/(7))`

Options

A. 58 cm
B. 48 cm
C. 38 cm
D. 28 cm

Answer

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

### Step 1: Understand the relationship between distance traveled and wheel rotations.
The distance traveled by the car is equal to the number of rotations of the wheel multiplied by the circumference of the wheel.

### Step 2: Write the formula for the circumference of the wheel.
The circumference \( C \) of a circle (or wheel) is given by the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius of the wheel.

### Step 3: Set up the equation for the total distance traveled.
Given that the wheel rotates 1000 times, the total distance \( D \) traveled can be expressed as:
\[ D = \text{Number of Rotations} \times \text{Circumference} \]
Substituting the known values:
\[ 1.76 \text{ km} = 1000 \times C \]

### Step 4: Convert kilometers to centimeters.
Since we need the radius in centimeters, we convert 1.76 km to centimeters:
\[ 1 \text{ km} = 1000 \text{ m} = 1000 \times 100 \text{ cm} = 100000 \text{ cm} \]
Thus,
\[ 1.76 \text{ km} = 1.76 \times 100000 \text{ cm} = 176000 \text{ cm} \]

### Step 5: Substitute the circumference formula into the distance equation.
Now we can substitute the circumference \( C \) into the distance equation:
\[ 176000 = 1000 \times (2 \pi r) \]

### Step 6: Simplify the equation.
Divide both sides by 1000:
\[ 176 = 2 \pi r \]

### Step 7: Solve for \( r \).
Now, substitute \( \pi \) with \( \frac{22}{7} \):
\[ 176 = 2 \times \frac{22}{7} \times r \]
Multiply both sides by \( \frac{7}{44} \) to isolate \( r \):
\[ r = \frac{176 \times 7}{44} \]

### Step 8: Calculate the value of \( r \).
Calculating the right side:
\[ r = \frac{176 \times 7}{44} = \frac{1232}{44} = 28 \text{ cm} \]

### Final Answer:
The radius of the wheel is \( 28 \text{ cm} \).

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