A cylinder in Calculus is not only a daily life cylinder that we know. It is a surface that is generated by moving a straight line along a given planar curve while holding the line parallel to a given fixed line.The curve is called a generating curve.
In other word, a 2D graph is extended. For example, the curve z = y2 in yz-plane is 'extended' to all values of x. The box below contains 3 different types of cylinders. Each cylinder is extended to different values of x, y or z. Take note of the corresponding 'base' at the right. According to the example z = y2 (Cylinder 3), its 'base' is on yz-plane (check with the axes labels), then the 'base' is 'extended' to all values of x. Slide the value a, b or c to play around with the graph. If you wish to rotate the 3D graph, just click here.
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