The radius of a circular wheel is 1.75 m. The number of revolutions it will make in travelling 11 km is :
(use `pi = (22)/(7)`)

Options

A. 800
B. 900
C. 1000
D. 1200

Answer

To find the number of revolutions a circular wheel makes while traveling a certain distance, we can follow these steps:

### Step 1: Calculate the circumference of the wheel
The circumference \( C \) of a circle is calculated using the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

Given:
- Radius \( r = 1.75 \) m
- \( \pi = \frac{22}{7} \)

Substituting the values into the formula:
\[ C = 2 \times \frac{22}{7} \times 1.75 \]

### Step 2: Simplify the calculation
First, calculate \( 2 \times \frac{22}{7} \):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
Now, multiply this by the radius:
\[ C = \frac{44}{7} \times 1.75 \]

To multiply \( 1.75 \) by \( \frac{44}{7} \), convert \( 1.75 \) to a fraction:
\[ 1.75 = \frac{7}{4} \]
Now, multiply:
\[ C = \frac{44}{7} \times \frac{7}{4} = \frac{44 \times 7}{7 \times 4} = \frac{44}{4} = 11 \text{ m} \]

### Step 3: Convert the distance traveled into meters
The distance traveled is given as 11 km. We need to convert this into meters:
\[ 11 \text{ km} = 11 \times 1000 = 11000 \text{ m} \]

### Step 4: Calculate the number of revolutions
The number of revolutions \( N \) can be calculated using the formula:
\[ N = \frac{\text{Distance traveled}}{\text{Circumference}} \]
Substituting the values we have:
\[ N = \frac{11000 \text{ m}}{11 \text{ m}} = 1000 \]

### Final Answer
The number of revolutions the wheel will make in traveling 11 km is:
\[ \boxed{1000} \]

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