The region bounded by the curves y = ± 4/√x and the lines x = 1 and x = 4 is revolved about the y-axis to generate a solid.

a. Find the volume of the solid.

b. Find the center of mass of a thin plate covering the region if the plate’s density at the point (x, y) is δ(x) = 1/x.

c. Sketch the plate and show the center of mass in your sketch.