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Formulas help you find the volume of other regular shapes, such as
spheres and cylinders. All the measurements used in a volume formula
must be made in the same length units. The units for volume are often
expressed in terms of cubic units, that is, a length to the third power,
such as meters or centimeters cubed.
Measuring Volume by Displacement
Not all objects have a regular shape. There is no simple formula
for calculating the volume of something with an irregular
shape. Instead, you can make use of a simple fact: two objects
cannot take up the same space at the same time. This method
of measuring is called displacement. That is because the object
being measured displaces, or takes the place of, liquid in a
container during the measurement process. The process is
described below.
1
Add water to a graduated cylinder. Note the volume.
2
Submerge the object in the water. The water level goes up.
Note the new volume of the water with the object in it.
3
water
rises
Subtract the volume of the water before the object was
added (found in step 1) from the volume of the water and
the object together (found in step 2). The difference is the
volume of the object. The object displaces a volume of
water equal to the volume of the object.
The volume of a liquid is often measured in milliliters (mL).
One milliliter of water has a volume of one cubic centimeter.
Milliliters and cubic centimeters are equivalent. In other words,
1 mL = 1 cm3.
Measure the
volume of water
without the rock.
Measure the
volume of water
with the rock in it.
Density is mass divided by volume.
As discussed earlier, a bowling ball and a basketball are about the
same size. But the bowling ball has a much greater mass. This example
can help you understand the concept of density. Density is a measure
of the amount of matter present in a given volume of a substance.
Density describes how closely packed matter is. The bowling ball is
much denser than the basketball.
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Learn more about
density.
Density depends on both the mass and the volume of an object.
If you cut a bar of gold in half, you would have two bars with half the
mass of the original bar. However, each bar would also have half the
volume of the original bar. The density of gold does not change. The
density of a substance does not depend on how much of it you have.
A bar of gold and a nugget of gold have the same density.
Chapter 4: Density and Buoyancy 105
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