A circular racing track is such that its outer circumference measures `"440 m"` and its inner circumference is `"396 m"`. Find the width of the track.

Options

A. `10 m`
B. `9 m`
C. `8 m`
D. `7 m`

Answer

To find the width of the circular racing track, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given circumferences:**
- Outer circumference (C1) = 440 m
- Inner circumference (C2) = 396 m

2. **Use the formula for circumference of a circle:**
The circumference (C) of a circle is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

3. **Calculate the outer radius (r1):**
Using the outer circumference:
\[ C1 = 2\pi r1 \]
Substituting the value of C1:
\[ 440 = 2\pi r1 \]
Rearranging to find \( r1 \):
\[ r1 = \frac{440}{2\pi} \]
Using \( \pi \approx \frac{22}{7} \):
\[ r1 = \frac{440}{2 \times \frac{22}{7}} = \frac{440 \times 7}{44} = 70 \text{ m} \]

4. **Calculate the inner radius (r2):**
Using the inner circumference:
\[ C2 = 2\pi r2 \]
Substituting the value of C2:
\[ 396 = 2\pi r2 \]
Rearranging to find \( r2 \):
\[ r2 = \frac{396}{2\pi} \]
Again using \( \pi \approx \frac{22}{7} \):
\[ r2 = \frac{396}{2 \times \frac{22}{7}} = \frac{396 \times 7}{44} = 63 \text{ m} \]

5. **Calculate the width of the track:**
The width of the track is the difference between the outer radius and the inner radius:
\[ \text{Width} = r1 - r2 = 70 \text{ m} - 63 \text{ m} = 7 \text{ m} \]

### Final Answer:
The width of the track is **7 m**.