Geometric Surfaces: Prisms and Cylinders

Prisms

A prism is a polyhedron whose faces consist of two congruent polygons lying in parallel planes and a number of parallelograms. The sides of the parallelograms are the segments that join the corresponding vertices of the two congruent polygons. These two congruent polygons are called the bases of the prism. The parallelograms are called the lateral faces of the prism. The segments that join the bases and form the sides of the lateral faces are called the lateral edges of the prism. The union of the two polygons and the parallelograms form the entire prism.

Some obvious questions come up at this point. How many lateral faces are in a prism? The number of lateral faces is equal to the number of sides in the bases. If the bases are quadrilaterals, for example, then there will be four lateral faces. Why are the lateral faces parallelograms? The reason is that the bases lie in parallel planes. The segments joining them (the sides of the lateral faces), are parallel to each other, and the sides of the congruent polygons are parallel to each other. A pair of segments and a pair of sides make up the sides of the lateral faces, so each lateral face is a parallelogram.

In the figure above, the polygons ABCDE and FGHIJ are the bases of the prism. They are congruent and lie in parallel planes. The lateral faces, like quadrilateral JEDI, for example, are parallelograms.

One special kind of prism is a right prism. In a right prism, the lateral faces are all rectangles, and the lateral edges are perpendicular to the planes that contain the bases. One example of a right prism is a cube. A cube is a six-sided polyhedron whose faces are all congruent squares. Below a right prism is drawn:

Cylinders

Prisms are only one member in a larger group of geometric surfaces. That larger group is the set of cylinders. A cylinder is a surface that consists of two congruent simple closed curves lying in parallel planes and the segments that connect them. If these simple closed curves were polygons, then the cylinder would be a prism. Here is a drawing of a cylinder.

The parallel simple closed curves are the bases of the cylinder, and the segments that complete the cylinder form the lateral surface. Each segment in the lateral surface lies in a line, and each of these lines is parallel to the others that span the lateral surface. For example, in the figure above, the segment AB lies in a line that is parallel to the line that contains the segment BC. All of the segments that compose the lateral surface lie in such parallel lines.

We've already talked about cylinders whose bases are polygons. Another kind of cylinder with a special base is a circular cylinder. As you may have already guessed, a circular cylinder is a cylinder with circular bases. In addition to that, a right circular cylinder is a circular cylinder whose lateral surface contains segments that are perpendicular to the bases. A right circular cylinder is drawn below.