The solid S has a base region B defined by the curves y = 5x − x 2 and y = x. (A) Find the volume of S if the cross-sections through S perpendicular to the x-axis are squares with an edge along the base. (B) Find the volume of S if the cross-sections through S perpendicular to the x-axis are equilateral triangles with an edge along the base. 3 (C) Find the volume of S if the cross-sections through S parallel to the x-axis are semicircles with their diameter along the base. (D) Find the volume of S if the cross-sections through S parallel to the x-axis are isosceles right triangles with a leg along the base.