Final answer:
The volume of the solid generated by revolving the region between f(x) = sqrt(x) and the x-axis, for x in [0, 16], around the line y=5 is found using the washer method with the integral V = π ∫₀¹⁶ [(5 - sqrt(x))^2 - 25] dx.
Step-by-step explanation:
To find the volume of the solid generated by revolving the region between the curve f(x) = sqrt(x) and the x-axis, over the interval [0, 16], around the line y=5, you need to use the disk method or the washer method with vertical integration, because the axis of revolution is horizontal and parallel to the x-axis. When the region is revolved about a line other than the x-axis or y-axis, we must account for the distance from the curve to the axis of revolution.
The washer method involves calculating the volume of a series of thin washers (disks with holes), which when added up give the volume of the solid. The outer radius R of a washer will be 5 - f(x), because the line of revolution, y=5, is 5 units above the x-axis, while the inner radius r is simply 5. The volume of each washer is π(R^2 - r^2)dx. Therefore, the integral setup to find the total volume V is V = π∫₀¹⁶ [(5 - sqrt(x))^2 - (5)^2] dx.