A 7 m wide road runs outside around a circular park, whose circumference is 176 m. The area of the road is :
[use `pi = (22)/(7)`]

Options

A. `1386 m^(2)`
B. `1472 m^(2)`
C. `1512 m^(2)`
D. `1760 m^(2)`

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
Given the circumference of the circular park is 176 m, we can use the formula for circumference:
\[ C = 2\pi r \]
Substituting the values:
\[ 176 = 2 \times \frac{22}{7} \times r \]
To isolate \( r \), we rearrange the equation:
\[ r = \frac{176 \times 7}{2 \times 22} \]
Calculating this gives:
\[ r = \frac{1232}{44} = 28 \text{ m} \]

### Step 2: Find the radius of the outer circle (including the road)
The road is 7 m wide, so the radius of the outer circle \( R \) is:
\[ R = r + 7 = 28 + 7 = 35 \text{ m} \]

### Step 3: Calculate the area of the outer circle
The area \( A \) of a circle is given by:
\[ A = \pi R^2 \]
Substituting the value of \( R \):
\[ A_{\text{outer}} = \frac{22}{7} \times (35)^2 \]
Calculating \( (35)^2 \):
\[ (35)^2 = 1225 \]
Now substituting this back into the area formula:
\[ A_{\text{outer}} = \frac{22}{7} \times 1225 \]
Calculating this gives:
\[ A_{\text{outer}} = \frac{26950}{7} = 3843 \text{ m}^2 \]

### Step 4: Calculate the area of the inner circle (the park)
Using the radius \( r = 28 \text{ m} \):
\[ A_{\text{inner}} = \pi r^2 = \frac{22}{7} \times (28)^2 \]
Calculating \( (28)^2 \):
\[ (28)^2 = 784 \]
Now substituting this back into the area formula:
\[ A_{\text{inner}} = \frac{22}{7} \times 784 \]
Calculating this gives:
\[ A_{\text{inner}} = \frac{17248}{7} = 2464 \text{ m}^2 \]

### Step 5: Calculate the area of the road
The area of the road is the difference between the area of the outer circle and the area of the inner circle:
\[ A_{\text{road}} = A_{\text{outer}} - A_{\text{inner}} = 3843 - 2464 \]
Calculating this gives:
\[ A_{\text{road}} = 1379 \text{ m}^2 \]

### Final Answer
The area of the road is \( 1379 \text{ m}^2 \).

---