Final answer:
The volume of the solid generated by revolving the region around the line x = 1 is found using the shell method, and the correct volume is 16/5π. This is option B in the provided choices.
Step-by-step explanation:
To calculate the volume of the solid generated by revolving the given region around the line x = 1, we can use the shell method. The region is bounded by the curve y = 6√x, the line y = 6, and the y-axis (x = 0). When revolving around the line x = 1, the radius of each shell is (1 - x), and the height is y = 6√x. The volume of each shell is therefore 2π(1 - x)y dx, and we integrate this from x = 0 to the x-value where y = 6, which is x = 36.
The integral becomes V = ∫036 2π(1 - x)(6√x) dx. Solving this integral gives us the volume. After calculation, the correct answer for the volume is 16/5π, which corresponds to option B.