If you go back to the beginning, keeping everything the same but changing curveplotter[t] = {cos[t], 3 t sin[t], 3 t} to curveplotter[t] = {f[t], g[t], 3 t} where f[t] and g[t] are any functions you care to use, then how do you know that the volume of the resulting tube measures out to 24 π cubic units?