f[u_, t_, c_] = {3 t, Pi - (4 t*(1/c)), u*(20/Pi)}; 
g[u_, t_,  d_] = {(Pi/2) Cos[((3/2) t) + Pi] + d, (Pi/2) Sin[((3/2) t) + Pi] + d,  u*(20/Pi)}; 
h[u_, t_, c_] = {3 u, 3 t, (10*Sin[u]^2 Cos[t - Pi/2]^2)}; 
Manipulate[ ParametricPlot3D[{h[u, t, c], g[u, t, d], f[u, t, c]}, {t, 0, Pi/2}, {u, 0,  Pi/2}, 
     Boxed -> False, AspectRatio -> 1, AxesLabel -> {x, y, z},  PlotRange -> All], {c, Pi/2, 3 Pi/2}, {d, Pi/2, 3 Pi/2}]

Before I begin, it is important to note that the names of the 
goods, x and y, correspond to the axes on which their level of 
consumption is shown.
The Price of good y is fixed related to income while the price 
of good x varies. The vertical plane that can be manipulated 
using the "c" control shows the budget constraint. An 
increasing "c" value corresponds to an increase in the quantity 
of x the consumer can afford, or a lower price.
The other dynamic surface, a part of a cylinder, slides up the 
Utility function, U(x,y) that is made up of the consumer's 
indifference curves. The intersections of these two curves are a 
visualization of the indifference curves.