For each volume problem, draw a picture of the solid. Also draw a thin cross-section or a cylindrical shell. Then show a sequence of logical steps involving an integral to compute the volume. Let D represent the region bounded by the parabola v = x? and the line y = x. Compute the volume of the solid formed when D is revolved about: a) the x-axis. b) the y-axis. c) theliney = 3. d) thelinex = 5. Derive the formula for the volume of a sphere with radius r using a) the disk method. b) the shell method. The base of a solid is the region bounded by the x-axis and the semicircle y = 16 x2. Each cross section perpendicular to the x-axis is a square. Find the volume of the solid