Measuring Volume and Density of Planets
Geometry
Unit Objective: Students will use volume and density formulas and apply scientific notation. Although
the activities were written for a Geometry course, they could easily be adapted for other courses.
Activity 1: Which is Bigger?
Objective: Students will determine volume of planets using a formula and scientific notation.
Wyoming Standards: Math 1.1-Students represent and apply real numbers in a variety of forms.
Math 1.2-Students apply the structure and properties of the real number system.
Math 2.2-Students communicate, using mathematical language, to analyze
properties and determine attributes of 2- and 3- dimensional objects.
Math 2.5-Students connect geometry with other mathematical topics.
Math 3.1-Students apply estimation and measurement using he appropriate
methods and units to solve problems involving length.
Sci 1.9-Students develop an understanding of scientific content through inquiry.
Sci 2.2-Students use inquiry to conduct scientific investigations.
Materials Needed: Planet data sheet, calculator, modeling clay, ruler, wax paper
Time: 35 minutes
Related Links: http://www.windows.ucar.edu/tour/link=/teacher_resources/galileo/3.html
http://en.wikipedia.org/wiki/List_of_solar_system_objects_by_mass
Directions: Briefly discuss the size of the planets noting Jupiter is the largest. Give a copy of the planet
data table to each students. Point out that Jupiter has the biggest diameter and the most mass.
Next write this question on the board: Which is Bigger...Jupiter or All the Other Planets Combined?
Discussion should begin immediately on how the group is to define “bigger”. Have the students discuss
ways we could determine this, leading them into a comparison of the volumes.
Students will need to review two ideas before they start their computations. First radius equals ½
diameter. You may have to review how to find half of a number when using scientific notation. Second
volume equals 4/3 times pi times radius cubed. You will have to review how to easily cube a scientific
notation number. The front of the term will be cubed. The exponent will be multiplied by 3.
For example: 2x104 cubed
=(2x2x2)x(104x104x104)
=(2x2x2)x104x3
=8x1012
Students could use their scientific notation key on their calculator but they would miss an opportunity
to gain experience with scientific notation and exponent properties.
In the first blank column on their table have the students calculate and record the volume for each
planet. After the students are finished calculating the volumes again discuss the question “Which is
Bigger”. To add the volumes it is best to use a calculator with scientific notation. Some students will
need assistance with this. Discuss the results when all the students are finished.
Another way to compare the volumes is to make clay models of each of the planets. A good scale to
use is 1000 km of diameter will be 1 mm of diameter on the clay model. Have the students work in
pairs to make models of all nine planets. They should place them on their wax paper when completed.
Using our scale Jupiter should be 143 mm or 14.3 cm in diameter and Pluto should be 2.3 mm in
diameter. When the models are finished again discuss “Which is Bigger”. To test their answer the
students can then combine the clay from the eight smaller planets and reshape them into a sphere to
compare with Jupiter.
Radius (km) Volume (km3) Mass (kg)
Density (kg/m3)
23
3.302 x 10
Planet
Mercury
Diameter (km)
4,800
Venus
12,100
4.87 x 1024
Earth
12,750
5.97 x 1024
Mars
6,800
6.42 x 1023
Jupiter
142,800
1.90 x 1027
Saturn
120,660
5.68 x 1026
Uranus
51,800
8.86 x 1025
Neptune
49,500
1.02 x 1026
Pluto
3,000
1.31 x 1022
Radius (km)
Volume (km3)
Planet
Diameter (km)
Mass (kg)
Mercury
4,800
3.302 x 1023
Venus
12,100
4.87 x 1024
Earth
12,750
5.97 x 1024
Mars
6,800
6.42 x 1023
Jupiter
142,800
1.90 x 1027
Saturn
120,660
5.68 x 1026
Uranus
51,800
8.86 x 1025
Neptune
49,500
1.02 x 1026
Pluto
3,000
1.31 x 1022
Density (kg/m3)
Activity 2: Density of Planets
Objective: The students will use their volume calculations and unit conversions to determine which
planets are the most dense.
Wyoming Standards: Math 1.1-Students represent and apply real numbers in a variety of forms.
Math 1.2-Students apply the structure and properties of the real number system.
Math 2.2-Students communicate, using mathematical language, to analyze
properties and determine attributes of 2- and 3- dimensional objects.
Math 2.5-Students connect geometry with other mathematical topics.
Math 3.2-Students demonstrate an understanding of metric and are able to
do conversion of units.
Sci 1.9-Students develop an understanding of scientific content through inquiry.
Sci 2.2-Students use inquiry to conduct scientific investigations.
Materials Needed: Data from Activity 1, calculator
Time: 25 minutes
Related Links: http://www.windows.ucar.edu/tour/link=/teacher_resources/galileo/3.html
http://en.wikipedia.org/wiki/List_of_solar_system_objects_by_mass
Directions: Review the concept of density as mass per unit volume. Using S.I. units mass would be
measured in kilograms and volume would be measured in cubic meters. Have the students predict
which planet would be the most dense. Discuss why they chose that particular planet.
Help the students find the density of Mercury. Point out that the units are critical. Mass must be in
kilograms. Volume must be in cubic meters. Students may need assistance getting their measurements
converted to the correct units. A scientific calculator is definitely needed for these calculations.
Once the group has found the density for Mercury have the students calculate the densities for the other
planets. As some students finish they can help assist others who are having difficulties. When
everybody is finished record the values in a table on the board and discuss the results.
Point out that water has a density of 1000 kg/m3. Discuss this fact in comparison to the results for the
planets. Which planets are more dense than water? Which planets are less dense? Why do you think
this is true?