Page 683 - Basic College Mathematics with Early Integers

9.5 VOLUME AND SURFACE AREA
Objective

Find the Volume and Surface
Area of Solids.
Objective Finding Volume and Surface Area of Solids

A convex solid is a set of points, S, not all in one plane, such that for any two points
A and B in S, all points between A and B are also in S. In this section, we will find
the volume and surface area of special types of solids called polyhedrons. A solid
formed by the intersection of a finite number of planes is called a polyhedron. The
box below is an example of a polyhedron.

vertex
face

face edge
Polyhedron

vertex edge

Each of the plane regions of a polyhedron is called a face of the polyhedron. If the
intersection of two faces is a line segment, this line segment is an edge of the poly-
hedron.The intersections of the edges are the vertices of the polyhedron.
Volume is a measure of the space of a region. The volume of a box or can, for
example, is the amount of space inside. Volume can be used to describe the amount
of juice in a pitcher or the amount of concrete needed to pour a foundation for a
house.
The volume of a solid is the number of cubic units in the solid.A cubic centime-
ter and a cubic inch are illustrated.

Actual size

Actual size

1 cm
1 inch
1 cm
1 cm
1 cubic centimeter 1 inch
1 inch
1 cubic inch

The surface area of a polyhedron is the sum of the areas of the faces of the
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polyhedron. For example, each face of the cube on the left above has an area of
1 square centimeter. Since there are 6 faces of the cube, the sum of the areas of the
faces is 6 square centimeters. Surface area can be used to describe the amount of
material needed to cover a solid. Surface area is measured in square units.

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