From the preceding section you learned the formulas for computing the areas of various plane figures. These plane areas are important in the computation of VOLUMES, as you will see later in this section.

When plane figures are combined to form a three-dimensional object, the resulting figure is

a solid. For example, three rectangles and two triangles may be combined as shown in figure 1-17. The flat surfaces of the solid figure are its FACES, the top and bottom faces are the BASES, and the faces forming the sides are the LATERAL FACES or SURFACES.

Some solid figures do not have any flat faces, and some have a combination of curved surfaces and flat surfaces. Examples of solids with curved surfaces include cylinders, cones, and spheres. Those solids having no flat faces include a great majority of natural objects, such as rocks, living matter, and many other objects that have irregular surfaces.

A solid figure whose bases or ends are similar, equal, and parallel polygons, and whose faces are parallelograms, is known geometrically as a PRISM. The name of a prism depends upon its base polygons. If the bases are triangles, as in figure 1-17, the figure is a TRIANGULAR PRISM. A RECTANGULAR PRISM has bases that are rectangles, as shown in figure 1-18. If the bases of a prism are perpendicular to the planes forming its lateral faces, the prism is a RIGHT prism.

A PARALLELEPIPED is a prism with parallelograms for bases. Since the bases are parallel to each other, this means that they cut the lateral faces to form parallelograms. If a parallelepipeds is a right prism and if its bases are rectangles, it is a rectangular solid. A CUBE is a rectangular solid in which all of the six rectangular faces are squares.

Figure 1-18.-Rectangular prism, showing its height when not a right prism.

In determining the volume of most solids, you should use the following general formula:

V =Bh

Where V = the volume

    B = the area of the base or end area

    h = the height of the solid (the

perpendicular height from its base)