A circular road runs around a circular ground. If the difference between the circumference of the outer circle and the inner circle is 66 metres, the width of the road is :
(Take `pi = (22)/(7)`)

Options

A. 10.5 metres
B. 7 metres
C. 5.25 metres
D. 21 metres

Answer

To solve the problem, we need to find the width of the road given the difference between the circumferences of the outer and inner circles.

### Step-by-Step Solution:

1. **Understand the Problem**:
We have two circles: an inner circle with radius \( r \) and an outer circle with radius \( R \). The width of the road is the difference between the radii of the outer and inner circles, which can be expressed as \( w = R - r \).

2. **Circumference Formula**:
The circumference \( C \) of a circle is given by the formula:
\[ C = 2 \pi r \]
For the inner circle, the circumference is \( C_{inner} = 2 \pi r \) and for the outer circle, it is \( C_{outer} = 2 \pi R \).

3. **Set Up the Equation**:
According to the problem, the difference between the circumferences of the outer and inner circles is 66 meters:
\[ C_{outer} - C_{inner} = 66 \]
Substituting the circumference formulas:
\[ 2 \pi R - 2 \pi r = 66 \]

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

5. **Solve for the Width**:
Now, we can express the width \( w \) as:
\[ w = R - r \]
Therefore, we can rewrite the equation as:
\[ 2 \pi w = 66 \]
Now, divide both sides by \( 2 \pi \):
\[ w = \frac{66}{2 \pi} \]

6. **Substitute the Value of \( \pi \)**:
Given \( \pi = \frac{22}{7} \), we substitute this value into the equation:
\[ w = \frac{66}{2 \times \frac{22}{7}} = \frac{66 \times 7}{44} \]

7. **Calculate the Width**:
Simplifying the expression:
\[ w = \frac{462}{44} = 10.5 \text{ meters} \]

### Final Answer:
The width of the road is **10.5 meters**.