Final answer:
The volume of the solid formed by rotating region S about the x-axis can be calculated using the Disk Method, involving integrating the area of circular cross-sections paralleling the area of a circle formula πr², adjusted for the function f(x) from x=0 to x=3.
Step-by-step explanation:
The student is asking about finding the volume of a solid formed by rotating a region S around the x-axis. To solve for volume of such a solid, one would typically use the Disk Method or Washer Method, which involves integrating the area of circular cross-sections. The provided formulas give guidance to ensure that the equations used are dimensionally consistent. For a cylinder, as can be related to this problem, the volume (V) is the cross-sectional area (A) times the height (h), as shown in formula V = Ah. Specifically, for a rotation around the x-axis, the cross-sectional area would be πr², and the limits of integration would be the x-values that the region spans. Thus, the volume of the solid would then be the integral from 0 to 3 of π times the square of the function f(x) representing the boundary of the region S with respect to x.