The image you uploaded contains a problem related to finding the volume of a solid. The base of the solid is bounded by the graph of $y = \sqrt{x}$ and $y = \frac{x}{2}$, and the cross-section perpendicular to the x-axis is a semicircle with a diameter running across the y-axis.

The task is to find the volume of the solid. Here's how we can approach it:

1. Identify the region in the base: The problem gives two curves, $y = \sqrt{x}$ and $y = \frac{x}{2}$. The area between these two curves will serve as the base of the solid.

2. Find the intersection points: To determine the bounds of integration, we need to find the points where these two curves intersect by solving $\sqrt{x} = \frac{x}{2}$.

3. Cross-sectional area: The cross-section is described as a semicircle, with its diameter along the line segment from the curve $y = \sqrt{x}$ to $y = \frac{x}{2}$. The formula for the area of a semicircle is $A = \frac{1}{2} \pi r^2$, where $r$ is the radius of the semicircle.

4. Set up the volume integral: Integrate the cross-sectional area over the range of x-values that correspond to the base region.

Let's proceed step by step.

Would you like to begin with finding the intersection points of the curves, or would you like a detailed explanation of the entire solution process?