Exercise 1 Page 447

We are asked to describe how we can find volumes and surface areas of three-dimensional figures. Let's start with the volumes.

Volume

The volume of a solid is the measure of the amount of space inside the solid. For example, the volume of a bathtub is the amount of water (usually in liters or cubic meters) that it can hold.

When we measure the volume of a solid, we try to use the formulas that we already know. Here are some of the formulas for the volume we have learned about so far.

Figure	Formula
Cone	$V = \frac{1}{3} π r^{2} h$
Cylinder	$V = π r^{2} h$
Sphere	$V = \frac{4}{3} π r^{3}$

Note that it is impossible to know the formula for the volume of every figure. In some cases, we may have to manage some other way. For example, when we have a composite figure, we can try to split it into figures that we know. Then we can calculate the volume of each figure separately and add them together to find the total volume of the composite figure.

Surface Area

The surface area of a figure, on the other hand, is the total area of all the surfaces of a shape. Suppose we are upholstering a couch. We would want to know its surface area so we could buy the right amount of fabric.

Just as before, there are formulas for the surface areas of the most common shapes.

Figure	Formula
Cone	S.A. $= π r ℓ + π r^{2}$
Cylinder	S.A. $= 2 π r h + 2 π r^{2}$
Sphere	S.A. $= 4 π r^{2}$

If a shape is not a common one, we can usually divide its surface into polygons so we can find the area of each polygon. We can then add the areas together to find the total surface area.