A road which is 7 m wide surrounds a circular park whose circumference is 88 m. Find the area of the road.

Answer

To find the area of the road surrounding the circular park, we can follow these steps:

### Step 1: Find the radius of the circular park.
The circumference (C) of the circular park is given as 88 m. We can use the formula for the circumference of a circle:
\[ C = 2\pi r \]
where \( r \) is the radius. Rearranging the formula to find the radius:
\[ r = \frac{C}{2\pi} \]
Substituting the value of C:
\[ r = \frac{88}{2\pi} = \frac{44}{\pi} \]

### Step 2: Calculate the radius of the circular park.
Using the approximate value of \( \pi \approx 3.14 \):
\[ r \approx \frac{44}{3.14} \approx 14.0 \text{ m} \]

### Step 3: Find the outer radius of the road.
The road is 7 m wide, so the outer radius (R) of the road surrounding the park can be calculated as:
\[ R = r + 7 \]
Substituting the value of \( r \):
\[ R = 14 + 7 = 21 \text{ m} \]

### Step 4: Calculate the area of the circular park.
The area (A) of the circular park can be calculated using the formula:
\[ A = \pi r^2 \]
Substituting the value of \( r \):
\[ A = \pi (14)^2 = \pi \times 196 \]
Using \( \pi \approx 3.14 \):
\[ A \approx 3.14 \times 196 \approx 384.64 \text{ m}^2 \]

### Step 5: Calculate the area of the larger circle (park + road).
The area of the larger circle can be calculated using the outer radius (R):
\[ A_{outer} = \pi R^2 \]
Substituting the value of \( R \):
\[ A_{outer} = \pi (21)^2 = \pi \times 441 \]
Using \( \pi \approx 3.14 \):
\[ A_{outer} \approx 3.14 \times 441 \approx 1385.94 \text{ m}^2 \]

### Step 6: Find the area of the road.
The area of the road can be found by subtracting the area of the circular park from the area of the larger circle:
\[ A_{road} = A_{outer} - A \]
Substituting the values:
\[ A_{road} \approx 1385.94 - 384.64 \approx 1001.30 \text{ m}^2 \]

### Final Answer:
The area of the road is approximately \( 1001.30 \text{ m}^2 \).

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