The radius of a wheel is 25 cm. How many rounds it will take to complete 11 km.

Options

A. 5000
B. 6000
C. 7000
D. 4000

Answer

To find out how many rounds a wheel with a radius of 25 cm will take to complete a distance of 11 km, we can follow these steps:

### Step 1: Calculate 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.

Given:
- Radius \( r = 25 \) cm
- Using \( \pi \approx \frac{22}{7} \)

Now, substituting the values:
\[ C = 2 \times \frac{22}{7} \times 25 \]

### Step 2: Simplify the Circumference Calculation
Calculating the circumference:
\[ C = 2 \times \frac{22}{7} \times 25 = \frac{1100}{7} \text{ cm} \]

### Step 3: Convert the Distance from Kilometers to Centimeters
The total distance to be covered is 11 km. We need to convert this distance into centimeters:
\[ 11 \text{ km} = 11 \times 1000 \text{ m} = 11 \times 1000 \times 100 \text{ cm} = 11,000,000 \text{ cm} \]

### Step 4: Calculate the Number of Rounds
To find the number of rounds \( N \), we use the formula:
\[ N = \frac{\text{Total Distance}}{\text{Circumference}} \]
Substituting the values we have:
\[ N = \frac{11,000,000 \text{ cm}}{\frac{1100}{7} \text{ cm}} = 11,000,000 \times \frac{7}{1100} \]

### Step 5: Simplify the Calculation
Calculating the number of rounds:
\[ N = \frac{11,000,000 \times 7}{1100} = \frac{77,000,000}{1100} = 70,000 \]

### Step 6: Final Calculation
Now, dividing \( 70,000 \) by \( 1000 \) (since we need the number of rounds):
\[ N = 7000 \]

Thus, the number of rounds the wheel will take to complete 11 km is **7000 rounds**.

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