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. **Calculate the area of a full circle:** \[ \text{Area of full circle} = \pi r^2 \] Substituting \( r = 2 \): \[ \pi (2)^2 = \pi \times 4 = 4\pi \] 2. **Find the area of the semicircle:** A semicircle is half of a full circle, so: \[ \text{Area of semicircle} = \frac{1}{2} \times \text{Area of full circle} = \frac{1}{2} \times 4\pi = 2\pi \] **Final Answer:** The area of one semicircular cross-section is \( 2\pi \) square units.