Volume & Density of Planets

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

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.

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

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?