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

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: \[ A \approx 2 \times 3.1416 = 6.2832 \ \text{square units} \]