When a force of 5 N acts on a surface, it produces a pressure of 500 Pa. The area of surface then must be :

Options

A. 10 `cm^(2)`
B. 50 `cm^(2)`
C. 100 `cm^(2)`
D. 0.01 `cm^(2)`

Answer

To solve the problem, we need to find the area of the surface when a force of 5 N produces a pressure of 500 Pa. We can use the formula for pressure, which is defined as:

\[ P = \frac{F}{A} \]

where:
- \( P \) is the pressure (in Pascals),
- \( F \) is the force (in Newtons),
- \( A \) is the area (in square meters).

### Step-by-step solution:

1. **Identify the given values**:
- Force \( F = 5 \, \text{N} \)
- Pressure \( P = 500 \, \text{Pa} \)

2. **Rearrange the formula to find the area**:
- From the formula \( P = \frac{F}{A} \), we can rearrange it to solve for \( A \):
\[ A = \frac{F}{P} \]

3. **Substitute the known values into the formula**:
\[ A = \frac{5 \, \text{N}}{500 \, \text{Pa}} \]

4. **Calculate the area**:
\[ A = \frac{5}{500} = 0.01 \, \text{m}^2 \]

5. **Convert the area from square meters to square centimeters**:
- We know that \( 1 \, \text{m} = 100 \, \text{cm} \), therefore:
\[ 1 \, \text{m}^2 = (100 \, \text{cm})^2 = 10000 \, \text{cm}^2 \]
- Thus, to convert \( 0.01 \, \text{m}^2 \) to square centimeters:
\[ A = 0.01 \, \text{m}^2 \times 10000 \, \text{cm}^2/\text{m}^2 = 100 \, \text{cm}^2 \]

6. **Conclusion**:
- The area of the surface is \( 100 \, \text{cm}^2 \).

### Final Answer:
The area of the surface is **100 cm²**.