Geometry and Trigonometry

Solid Geometry

How are some common solids defined?

There are numerous objects defined in solid geometry. The following lists the most common (and some interesting) ones:

Cone—A cone can be both a surface and a solid. A solid cone is bounded by a region enclosed in a closed curve on a plane and a surface formed by segments joining each point of the closed curve to a point that is not in the plane. (Note: Two solid cones seen with their pointed ends together help define conic sections; for more about conic sections, see elsewhere in this chapter.)

Pyramid—A pyramid is a polyhedron (see above) with one face a polygon and all other faces as triangles with a common endpoint (vertex). They are named based on the polygon’s base, such as the triangular pyramid, square pyramid, and so on. Some of the most famous “solid pyramids” are the sandstone pyramids of Egypt. These are actually called right square pyramids because the base of the polygon is a square and the vertical line from the vertex meets the center of the base.

Cylinder—A cylinder can be both a surface and a solid. A solid cylinder is one that forms by rotating a circle about an axis through the midpoints of the opposite side; it is also called a right circular cylinder. One of the most well-known cylinders is possibly sitting right next to you: A coffee cup, with its cylindrical shape, and the bases (in this case, the base and rim) considered to be congruent circles.

Prism—A prism is a polyhedron with two parallel, congruent faces that make up the bases of the shape; the other, lateral faces are considered to be parallelograms. If the lateral faces are rectangles, the prism is called a right prism.

Parallelepiped—This strange-sounding polyhedron is one that has all its faces as parallelograms, or a prism with parallelogram bases. The most familiar parallelepiped is a simple box—also called a rectangular parallelepiped—that has rectangles for all the six faces. (For more about these figures, including how to calculate their areas, see elsewhere in this chapter.)


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