CYLINDER CONSTRUCTION

The cylinder is a surface of revolution. The slice through a cylinder parallel to the base at any height is a circle of the same radius as the cylinder. Let r denote the radius of the cylinder and v be any height. Then, the parametric equation for the cylinder is (rcosu, rsinu, v). In determining the range of v for the cylinder, it is important to note where the origin is and where the cylinder is in relation to the origin.

The construction of this cylinder is based on measurements from a side-elevation. The radius is 6.40 cm, the height is 5.30 cm, and the origin is located at the center of the base of the base cone. Above the cylinder is the trapezoidal layer which has a measured height of 2.55 cm. Consequently, the top of the cylinder has v equal to -2.55 and the bottom has v equal to -2.55 - 5.30 = -7.85. Therefore, the parametric equation for this cylinder is:

Cylinder(u,v) = (6.40cosu, 6.40sinu, v)

where the range of v is [-7.85, -2.55] and that of u is [0, 2pi]. Notice that in the computer model image, the cylinder contains alternate segments that are left out in order to represent windows as seen in the side-elevation.

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