**Problem Statement:**Find the volume of the solid obtained by rotating the region bounded by \( y = \frac{1}{2}x \), the line \( x = 4 \), and the x-axis about the line \( y = 2 \). Round your answer to two decimal places.**Diagram Explanation:**This is a typical problem involving the application of the disk or washer method to find volumes of solids created by revolving regions around specific lines.1. **Boundaries:** - The line \( y = \frac{1}{2}x \) is a linear function, representing a straight line through the origin with a slope of \( \frac{1}{2} \). - The vertical line \( x = 4 \) forms the right boundary of the region. - The x-axis (where \( y = 0 \)) serves as the lower boundary. 2. **Rotation Axis:** - The line \( y = 2 \) is a horizontal line parallel to the x-axis, and it serves as the axis of rotation.Using these boundaries and the axis of rotation, you can apply the appropriate methods to calculate the volume of the solid by considering the horizontal distance between the curve and the axis of rotation.

To find the volume of the solid obtained by rotating the region bounded by , the line and the x-axis about the line .By using graphing utility, the region bounded by the curves , the line and the -axis, is shown by the shaded region (yellow color region) in the following figure.From the figure, We observe that the shaded region is bounded by the curves and from .We know that the volume of the solid obtained by rotating the region bounded bythe curves , from , about the line, , is given by Therefore, the volume of the solid obtained by rotating the region bounded bythe curves and , from about the line, , is given by Hence, the volume of the solid is 33.51 cubic units.The volume of the solid is 33.51 cubic units.