The top outer edge of a solid with vertical sides that is resting on the xy-plane is modeled by r(t) = 3 cos ti + 3 sin tj + (1 + sin² 2t)k, where all measurements are in centimeters. The intersection of the plane y = b, where -3 < b < 3, with the top of the solid is a horizontal line.
(a) Use a computer algebra system to graph the solid.
(b) Use a computer algebra system to approximate the lateral surface area of the solid.
(c) Find (if possible) the volume of the solid.