It´s possible to make a solid plot with different transversal section ?

For example, if we have to make a solid of revolution we just take the command "RevolutionPlot3D". But what happen when you need to plot a different solid with different transversal sections like triangles, square, ellipses, Etc.

It is capable mathematica to plot a solid whose characteristics are the following : The solid formed by a deformable circle whose center moves around the periphery of an ellipse. The radius of the circle measures the distance between the point (x,0) and (x,y), where "y" is defined as: y=(b / a) Sqrt(a^2 - x^2) (Ellipse)

Another example: The solid with circular base whose cross sections perpendicular to the diameter of the circle are square . The side of the square is defined as parallel to the diameter of the rope circumference. ( The side of the square is variable) .

So, If Mathematica is able to plot such solids. What kind of command should I use to draw it. Right now i´m using Wólfram Mathematica 10.