A circular track runs around a circular park . If the difference between the circumference of the track and the park is 66 cm , then find the width of the track .

Answer

To solve the problem, we need to find the width of the circular track that runs around the circular park, given that the difference between the circumferences of the track and the park is 66 cm.

### Step-by-Step Solution:

1. **Define the Variables:**
- Let the radius of the circular park be \( r \) (small r).
- Let the radius of the circular track be \( R \) (capital R).
- The width of the track is given by \( R - r \).

2. **Write the Formula for Circumference:**
- The circumference of the park (inner circle) is given by:
\[ C_{park} = 2\pi r \]
- The circumference of the track (outer circle) is given by:
\[ C_{track} = 2\pi R \]

3. **Set Up the Equation for the Difference in Circumference:**
- According to the problem, the difference between the circumferences of the track and the park is 66 cm:
\[ C_{track} - C_{park} = 66 \]
- Substituting the formulas for circumference:
\[ 2\pi R - 2\pi r = 66 \]

4. **Factor Out Common Terms:**
- We can factor out \( 2\pi \) from the left side:
\[ 2\pi (R - r) = 66 \]

5. **Solve for \( R - r \):**
- Divide both sides by \( 2\pi \):
\[ R - r = \frac{66}{2\pi} \]
- Using \( \pi \approx \frac{22}{7} \):
\[ R - r = \frac{66}{2 \times \frac{22}{7}} = \frac{66 \times 7}{44} = \frac{462}{44} = 10.5 \]

6. **Conclusion:**
- The width of the track is:
\[ R - r = 10.5 \text{ cm} \]

### Final Answer:
The width of the track is **10.5 cm**.