(a) Sketch the curve whose equation is y = (x – 2)(x – 1) Show that the volume generated when the finite area between the curve and the x axis is rotated through 2π radians about the x axis is π/30.

(b) Show that the curved surface generated by the revolution about the x axis of the portion of the curve y² = 4ax included between the origin and the ordinate x = 3a is 56/3πa².