The goal of this project is to find the volume of some shapes that come up in a variety of applications.

Part [1] The first shape is a torus, a donut shape. Let a be the distance from the center of the overall shape to center of the outer ring and b be the radius of the outer ring. Below is shown the torus along with a cross section view, the vertical axis is z and the horizontal axis is either x or y (note it is symmetric about the z- axis.) Find both a Cartesian and cylindrical representation of the torus (hint: one way is to find the equation of the little circle in terms of r and z to get the cylindrical equation then convert them to Cartesian.)

Part 3 picture below:

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