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 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: Calculate the circumference of the wheel
The circumference \( C \) of a circle is given by the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle. Given that the radius \( r = 1.75 \) m and using \( \pi = \frac{22}{7} \), we can calculate the circumference.

\[ C = 2 \times \frac{22}{7} \times 1.75 \]

### Step 2: Simplify the calculation
First, calculate \( 2 \times 1.75 \):
\[ 2 \times 1.75 = 3.5 \]
Now substitute this back into the circumference formula:
\[ C = \frac{22}{7} \times 3.5 \]

Next, convert 3.5 into a fraction:
\[ 3.5 = \frac{7}{2} \]
Now, substitute this value into the circumference formula:
\[ C = \frac{22}{7} \times \frac{7}{2} \]

### Step 3: Calculate the circumference
Now, simplify:
\[ C = \frac{22 \times 7}{7 \times 2} = \frac{22}{2} = 11 \text{ m} \]
So, the circumference of the wheel is 11 m.

### Step 4: Convert the distance traveled into meters
The distance traveled is given as 11 km. We need to convert this into meters:
\[ 11 \text{ km} = 11,000 \text{ m} \]

### Step 5: Calculate the number of revolutions
The number of revolutions \( N \) can be calculated using the formula:
\[ N = \frac{\text{Total Distance}}{\text{Circumference}} \]
Substituting the values we have:
\[ N = \frac{11,000 \text{ m}}{11 \text{ m}} = 1,000 \]

### Final Answer
The number of revolutions the wheel will make while traveling 11 km is **1,000**.

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