To calculate the area in square meters, we use the formula for the area of a circle:

\[
A = \pi r^2
\]

### Given Data:
- Radius of the piston face, \( r = 400 \, \text{mm} \).

First, convert the radius to meters:

\[
r = 400 \, \text{mm} = 0.4 \, \text{m}
\]

### Step-by-Step Calculation:
1. Plug the value of \( r \) into the formula:

   \[
   A = \pi \times (0.4)^2
   \]

2. Using \( \pi \approx 3.142 \):

   \[
   A = 3.142 \times 0.16
   \]

3. Calculate the area:

   \[
   A = 0.50272 \, \text{m}^2
   \]

### Final Answer:
The area of the piston face is **0.50272 m²**.

Would you like further details or have any questions?

### Related Questions:
1. How do you calculate the area if the diameter is given instead of the radius?
2. How does the area change if the radius is halved?
3. What is the formula for calculating the circumference of a circle?
4. How would you calculate the volume of a cylinder using the area of the piston face?
5. What are some common applications of calculating areas in engineering?

### Tip:
Remember that squaring the radius has a significant effect on the area because it multiplies the radius value twice, making the area grow faster than the radius itself.

Learn how to calculate the area of a circle with a radius of 400 mm using the formula A = πr^2. Step-by-step solution included.

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