Example 1-4 Combining Volumes
What is the volume (in cubic kilometers) of Earth? What is the volume of the Moon? What is the combined volume of the
two worlds together? The radius of Earth is 6378 km, and the radius of the Moon is 1738 km.
Set Up
From the Math Tutorial, the volume of a sphere of radius
R is 4pR3 >3. Since we multiply the radius by itself, the
­answer can have no more significant figures than the
value of the radius.
Radius of Earth RE = 6378 km
Radius of Moon RM = 1738 km
Solve
Volume of Earth:
4p 16378 km2 3
VE =
3
= 1.086781293 * 1012 km3
For Earth, RE has four significant figures, so the volume
has only four significant figures.
Round to four significant figures:
VE = 1.087 * 1012 km3
The radius of the Moon also has four significant figures,
and so its volume does as well.
Volume of Moon:
4p 11738 km2 3
VM =
3
= 2.199064287 * 1010 km3
Round to four significant figures:
VM = 2.199 * 1010 km3
To find the combined volume, we add VE and VM. To
make sure we retain the correct number of significant
figures in our answer, we express both numbers in
scientific notation with the same exponent. According
to Rule 2 for addition, our answer must have only three
significant figures to the right of the decimal point.
VE = 1.087  1012 km3
VM = 2.199  1010 km3
= 0.02199  1012 km3
To avoid intermediate rounding errors we will use the
­unrounded values and then round the result to three
digits to the right of the decimal point at the end of the
calculation.
VE + VM = (1.086781293  1012 km3)
+ (0.02199064287  1012 km3)
= (1.086781293 + 0.02199064287)  1012 km3
= 1.10877193587  1012 km3
This has too many significant figures, so we round to the
final answer of
VE + VM = 1.109  1012 km3
Reflect
In this problem we had to use both the significant figure rule for multiplication and the significant figure rule for
addition. You should be prepared to use both of these rules in solving problems on your own. In this example, if we had
used the rounded values of the volumes, we would have gotten VE + VM = 1.087  1012 km3 + 0.02199  1012 km3 =
1.10899  1012 km3, which still rounds to 1.109  1012 km3. But this is not always the case, so don’t round until you
have finished all your calculations.