The radius of a circular wheel is 1.75 m. How many revolutions will it make in travelling 11 km?

Options

A. 10
B. 100
C. 1000
D. 10000

Answer

To solve the problem of how many revolutions a circular wheel with a radius of 1.75 m will make while traveling 11 km, we can follow these steps:

### Step 1: Find the Circumference of the Wheel
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
Where \( r \) is the radius of the circle.

Given:
- Radius \( r = 1.75 \) m

Substituting the value of \( r \):
\[ C = 2 \times \pi \times 1.75 \]
Using \( \pi \approx \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 1.75 \]

Calculating:
\[ C = 2 \times \frac{22 \times 1.75}{7} = 2 \times \frac{38.5}{7} = \frac{77}{7} \approx 11 \text{ m} \]

### Step 2: Convert Distance from Kilometers to Meters
We need to convert the distance traveled from kilometers to meters.

Given:
- Distance = 11 km

Converting kilometers to meters:
\[ 11 \text{ km} = 11 \times 1000 = 11000 \text{ m} \]

### Step 3: Calculate the Number of Revolutions
To find the number of revolutions \( N \), we can use the formula:
\[ N = \frac{\text{Distance traveled}}{\text{Circumference of the wheel}} \]

Substituting the values:
\[ N = \frac{11000 \text{ m}}{11 \text{ m}} = 1000 \]

### Final Answer
The wheel will make **1000 revolutions** while traveling 11 km.

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