AMSCO'S Geometry. New York - Rye High School

446 The Geometry of Three Dimensions11-5 VOLUME OF A PRISMA cube whose edges each measure 1 centimeteris a unit of volume called a cubic centimeter.If the bases of a rectangular solid3measure 8 centimeters by 5 centimeters, weknow that the area of a base is 8 5 or 40square centimeters and that 40 cubes each5with a volume of 1 cubic centimeter can fill8one base. If the height of the solid is 3 centimeters,we know that we can place 3 layers with 40 cubic centimeters in eachlayer to fill the rectangular solid. The volume of the solid is 40 3 or 120 cubiccentimeters.The volume of the rectangular solid is the area of the base times theheight. This can be applied to any prism and suggests the following postulate.Postulate 11.5The volume of a prism is equal to the area of the base times the height.If V represents the volume of a prism, B represents the area of the base, andh the height of the prism, then:V BhHGRED8 cmFC10 cmP15 cmNQ10 cmA15 cmBL16 cmMThe figure shows two prisms. One is a parallelepiped with parallelogramsABCD and EFGH as bases and rectangular faces ABFE, BCGF, CDHG, andDAEH. If AB is 15 centimeters and the length of the altitude from D to AB is8 centimeters, then the area of the base ABCD is 15 8 or 120 square centimeters.If BF, the height of the parallelepiped, is 10 centimeters, then:Volume of the parallelepiped 5 Bh5 120 3 105 1,200 cubic centimeters