Chapter 6: Figures in Space
Figures in space are called polyhedrons. A polyhedron is a three-dimensional figure with polygonal regions as its faces. There are mainly five types of polyhedrons. They are prisms, cylinder, pyramid, cone, and sphere. We are going to talk about each one of them in following paragraphs.
A prism is a polyhedron with two congruent polygonal faces, called the bases, in parallel planes. The remaining faces, called the lateral faces, are parallelograms. Each lateral face shares an edge with each of the bases. The lateral area of a right prism is the product of the perimeter of a base and the length of an altitude (L = ph). The volume of a prism is the product of the area of a base and the length of an altitude (V = Bh).
A cylinder is similar to a prism except that the two bases of a cylinder are circles instead of polygons. The total area of a right cylinder with radius of length r and altitude of length h is 2P r2 + 2P rh. The volume of a cylinder is Bh.
A pyramid is a polyhedron composed of a polygonal region, called the base, and triangular regions, called the lateral faces. The lateral faces intersect in a common point called the vertex. The intersections of each pair of lateral faces are the lateral edges. The altitude of the pyramid is the segment from the vertex to the plane containing and perpendicular to the base. The lateral area of a regular pyramid is one-half the product of the perimeter of the base and the slant height (L = 1/2pl). The volume of a pyramid is one-third the volume of a prism with the same base and altitude as the pyramid. The volume of a cone is one-third the volume of a cylinder with the same base and altitude as the cone (V = 1/3Bh).
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