Find the volume of the solid generated when the region bounded by y equals 8 x and y equals 32 startroot x endroot is revolved about the x-axis. a coordinate system has an unlabeled horizontal x-axis and an unlabeled vertical y-axis. from left to right, a curve labeled y equals 32 startroot x endroot starts on the origin and rises at a decreasing rate in quadrant 1. a line labeled y equals 8 x starts at the origin and rises from left to right, intersecting the curve at the origin and in quadrant 1. the region above the line and below the curve is shaded and labeled r. a curved arrow is rotated about the x-axis. x y y equals 32 startroot x endroot y equals 8 x upper r