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### 6-5. Polyhedra

#### 6-5-1. Volume and Area of a Solid

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By geometric solid we mean a closed surface in space. Sometimes the word solid is taken to mean the surface, and sometimes the surface itself together with its interior. Keep in mind that we are talking about geometric figures and not real objects, and the word solid should not be taken here in its usual sense to imply rigidity, as in "solid as a rock." We will refer to a soap bubble, for instance, as a spherical solid even though the soap film and the enclosed air are far from rigid.

The volume of a solid is a measure of the space it occupies or encloses. A cube of side 1 unit has a volume of 1 cubic unit, and we can think of the volume of any solid as the number of such cubes it contains. This may not be a whole number or even a rational number, as we will see with the volumes of cylinders and spheres.