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Section 3.1 Volume and Surface Area
For every 3-dimensional shape, we want to answer two fundamental questions:
How much space does it take up?
How much surface does it have?
These are the ideas of volume and surface area.
Volume is the amount of space a 3-dimensional object occupies. It is measured in cubic units, such as
\(\text{cm}^3\) or
\(\text{m}^3\text{.}\)
Surface area is the total area of the boundary of a 3-dimensional object. It is measured in square units, such as
\(\text{cm}^2\) or
\(\text{m}^2\text{.}\)
Volume tells you how much water a container can hold.
Surface area tells you how much paint you need to cover it.
Remark 3.1.1 . Units.
We will analyze the volume and surface area of a bunch of different 3-dimensional shapes. These shapes fall into 2 families, plus 1 special shape.
The
prism family includes shapes with 2 identical bases connected by flat (or curved) sides:
Cubes and rectangular prisms
More general prisms (e.g. with a triangular base)
Cylinders (a prism with a circular base)
The
pyramid family consists of shapes that meet up at a point at the top:
Cones (a pyramid with a circular base)
The
sphere stands on its own, as it has no base and no edges.
