The cross-section of a tunnel is a square of side 7 m surmounted by a semicircle. The tunnel is 80 m long Calculate : the surface area of the tunnel (excluding the floor) .

Answer

To calculate the surface area of the tunnel (excluding the floor), we will follow these steps:

### Step 1: Understand the shape of the tunnel
The cross-section of the tunnel consists of a square of side 7 meters, surmounted by a semicircle. The tunnel has a length of 80 meters.

### Step 2: Calculate the area of the semicircle
1. **Find the radius of the semicircle**:
- The diameter of the semicircle is equal to the side of the square, which is 7 meters.
- Therefore, the radius \( r \) is:
\[ r = \frac{7}{2} = 3.5 \text{ meters} \]

2. **Calculate the area of the semicircle**:
- The area \( A \) of a semicircle is given by the formula:
\[ A = \frac{1}{2} \pi r^2 \]
- Substituting the radius:
\[ A = \frac{1}{2} \times \frac{22}{7} \times (3.5)^2 \]
- Calculate \( (3.5)^2 = 12.25 \):
\[ A = \frac{1}{2} \times \frac{22}{7} \times 12.25 = \frac{22 \times 12.25}{14} = \frac{269.5}{14} \approx 19.9643 \text{ m}^2 \]

### Step 3: Calculate the area of the two side walls
1. **Calculate the area of one side wall**:
- The area of one wall is given by the formula:
\[ \text{Area of one wall} = \text{height} \times \text{length} = 7 \times 80 = 560 \text{ m}^2 \]

2. **Calculate the area of both side walls**:
- Since there are two walls:
\[ \text{Total area of both walls} = 2 \times 560 = 1120 \text{ m}^2 \]

### Step 4: Calculate the total surface area of the tunnel (excluding the floor)
1. **Add the area of the semicircle and the area of the two walls**:
- The total surface area \( S \) is given by:
\[ S = \text{Area of semicircle} + \text{Area of both walls} \]
- Substituting the values:
\[ S = 19.9643 + 1120 = 1139.9643 \text{ m}^2 \]

### Step 5: Round off the answer
- The total surface area of the tunnel (excluding the floor) is approximately:
\[ S \approx 1140 \text{ m}^2 \]

### Final Answer
The surface area of the tunnel (excluding the floor) is approximately **1140 m²**.

---