A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of `115^@` . Find the total area cleaned at each sweep of the blades.

Explanation

To find the total area cleaned by the two wipers of a car, we can follow these steps:

### Step 1: Understand the Problem
Each wiper has a blade length of 25 cm and sweeps through an angle of 115 degrees. We need to find the area cleaned by both wipers.

### Step 2: Calculate the Area of One Wiper's Sweep
The area cleaned by one wiper can be calculated using the formula for the area of a sector of a circle:
\[ \text{Area} = \frac{\theta}{360^\circ} \times \pi r^2 \]
Where:
- \(\theta\) is the angle in degrees (115 degrees)
- \(r\) is the radius (length of the wiper blade, which is 25 cm)

### Step 3: Substitute the Values
Substituting the values into the formula:
\[ \text{Area} = \frac{115}{360} \times \frac{22}{7} \times (25)^2 \]
Calculating \(25^2\):
\[ 25^2 = 625 \]
Now substituting this back into the area formula:
\[ \text{Area} = \frac{115}{360} \times \frac{22}{7} \times 625 \]

### Step 4: Simplify the Fraction
To simplify \(\frac{115}{360}\):
- Divide both the numerator and denominator by 5:
\[ \frac{115 \div 5}{360 \div 5} = \frac{23}{72} \]
Now substitute this back into the area formula:
\[ \text{Area} = \frac{23}{72} \times \frac{22}{7} \times 625 \]

### Step 5: Calculate the Total Area for Both Wipers
Since there are two wipers, the total area cleaned will be:
\[ \text{Total Area} = 2 \times \text{Area of one wiper} \]
Thus:
\[ \text{Total Area} = 2 \times \left(\frac{23}{72} \times \frac{22}{7} \times 625\right) \]

### Step 6: Simplify Further
Now, we can simplify:
\[ \text{Total Area} = \frac{2 \times 23 \times 22 \times 625}{72 \times 7} \]
Calculating \(72 \div 2 = 36\):
\[ \text{Total Area} = \frac{23 \times 22 \times 625}{36 \times 7} \]

### Step 7: Calculate the Final Value
Now we can compute the values:
- Calculate \(23 \times 22 = 506\)
- Then multiply by 625:
\[ 506 \times 625 = 316250 \]
- Now calculate \(36 \times 7 = 252\)
- Finally, divide:
\[ \text{Total Area} = \frac{316250}{252} \approx 1254.96 \text{ cm}^2 \]

### Final Answer
The total area cleaned at each sweep of the blades is approximately \(1254.96 \text{ cm}^2\).

---