If a solid has semicircular cross-sections with a radius of $$ r = 2 $$, find the area of one semicircular cross-section.

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To find the area of a semicircular cross-section with a radius $$ r = 2 $$, follow these steps:

1. **Understand the Formula for the Area of a Circle:**

The area $$ A $$ of a full circle is given by:
   $$
   A_{\text{circle}} = \pi r^2
   $$
   
2. **Determine the Area of a Semicircle:**

A semicircle is half of a full circle. Therefore, the area $$ A_{\text{semicircle}} $$ is:
   $$
   A_{\text{semicircle}} = \frac{1}{2} \times A_{\text{circle}} = \frac{1}{2} \pi r^2
   $$
   
3. **Plug in the Given Radius:**

Given $$ r = 2 $$:
   $$
   A_{\text{semicircle}} = \frac{1}{2} \pi (2)^2 = \frac{1}{2} \pi \times 4 = 2\pi
   $$
   
4. **Conclusion:**

The area of one semicircular cross-section with radius 2 is:
   $$
   A = 2\pi \ \text{square units}
   $$

If you prefer a numerical approximation:
   $$
   A \approx 2 \times 3.1416 = 6.2832 \ \text{square units}
   $$
The area of one semicircular cross-section with a radius of 2 is $$ 2\pi $$ square units, which is approximately 6.2832 square units.

If a solid has semicircular cross-sections with a radius of , find the area of one semicircular cross-section.

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