To solve the expression \( A = 2\pi \cdot 10(10 + 30) \), we proceed step by step:

### Step 1: Simplify the expression inside the parentheses.
\[
10 + 30 = 40
\]

### Step 2: Multiply by 10.
\[
10 \cdot 40 = 400
\]

### Step 3: Multiply by \( 2\pi \).
\[
A = 2\pi \cdot 400 = 800\pi
\]

So, the final value of \( A \) is:
\[
A = 800\pi \quad \text{(exact form)}
\]
or approximately:
\[
A \approx 2513.27
\]

Would you like further details or have any questions?

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Here are some related questions:
1. What is the significance of \( \pi \) in this equation?
2. How would this change if the multiplier was 5 instead of 10?
3. Can we interpret this geometrically, such as in a circle formula?
4. How does changing the parentheses grouping affect the result?
5. What is the meaning of an exact form like \( 800\pi \)?

**Tip:** Always simplify within parentheses first when working with expressions like this!

Learn how to solve the expression A = 2π * 10(10 + 30) with detailed steps, including simplifying parentheses, multiplying, and working with π. Suitable for students in Grades 6-8.

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