Final answer:
The student is tasked with finding the volume V of a solid created by rotating a given region around a specified line, using the appropriate volume formulas based on the identified curves and axis of rotation.
Step-by-step explanation:
The question is asking to find the volume V of a solid obtained by rotating a region bound by certain curves around a specified line. To sketch the region, one needs to identify the area between the curves y = 5x and y = 5. The volume can be found using the method of cylindrical shells or the disk/washer method, depending on the axis of rotation, employing formulas based on the function endpoints and the axis of rotation.
For a cylinder, the volume V is the cross-sectional area A times the height h, as described by the equation V = Ah. If the volume changes, such as when a piston compresses the contents of a cylinder, the new volume V is found by multiplying the area A by the new height h.