24. Sketch the region bounded by the curves x + y = 3, 2x + y = 6, x = 0, and find the volume of the solid generated by revolving this region about the y-axis.

28. The base of a solid is the region bounded by the ellipse 4x² + 9y² = 36. Find the volume of the solid given that cross sections perpendicular to the x-axis are (a) equilateral triangles; (b) squares.

30. The base of a solid is the region between the parabolas x = y² and x = 3 – 2y². Find the volume of the solid given that the cross sections perpendicular to the x-axis are (a) rectangles of height h; (b) equilateral triangles; (c) isosceles right triangles each with hypotenuse on the xy-plane.

38. Find the volume enclosed by the surface that is generated by revolving the equilateral triangle with vertices (0,0), (a,0), (a/2,3^1/2a/2) about the x-axis.

58. Find the volume when the region bounded by the curves y = x^3/2, x = 0, y = 8, is revolved about: (a) the y-axis; (b) the line y = 8; (c) the line x = 4; (d) the x-axis.