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.