To solve the expression \( \pi \times 42 \, \text{cm}^2 \times 42 \), follow these steps:

### Step-by-Step Calculation

1. **Simplify the expression:**

   \[
   \pi \times 42 \, \text{cm}^2 \times 42 = \pi \times 42 \times 42 \, \text{cm}^2
   \]

2. **Calculate \( 42 \times 42 \):**

   \[
   42 \times 42 = 1764
   \]

3. **Multiply by \( \pi \):**

   \[
   \pi \times 1764 \, \text{cm}^2 \approx 3.1416 \times 1764 \, \text{cm}^2
   \]

4. **Final Result:**

   \[
   \pi \times 1764 \, \text{cm}^2 \approx 5541.77 \, \text{cm}^2
   \]

### Answer:
\[
\pi \times 42 \, \text{cm}^2 \times 42 \approx 5541.77 \, \text{cm}^2
\]

Would you like more details on this calculation, or do you have any further questions?

Here are five related questions:
1. What is the value of \( \pi \) and why is it used in calculations?
2. How do you calculate the area of a circle using \( \pi \)?
3. Can \( \pi \) be expressed as a fraction?
4. How does multiplying a value by \( \pi \) affect the result?
5. What are common geometric applications of \( \pi \)?

**Tip:** When using \( \pi \) in calculations, you can either use \( \pi \approx 3.1416 \) for approximate results or keep \( \pi \) in its symbolic form for exact answers.

Solve the expression π × 42 cm² × 42 step by step. This calculation covers the multiplication of the constant π and involves geometric area concepts. Suitable for Grades 6-8 students studying basic geometry and pi (π) applications.

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