Activity 3: The Capacity of the Planets (Grades 8-12)

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Objective:
The students will demonstrate the ability to represent numbers in scientific notation and use geometry to solve problems about planets in the solar system.

NCTM Standards:

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems;
• Understand the meaning of operations and how they relate to each other;
• Use computational tools and strategies fluently and estimate appropriately.
• Analyze characteristics and properties of two- and three-dimensional geometric objects;
• Select and use different representational systems, including coordinate geometry and graph theory;
• Recognize the usefulness of transformations and symmetry in analyzing mathematical situations;
• Use visualization and spatial reasoning to solve problems both within and outside of mathematics

The Capacity of the Planets

In this activity, students use information about three-dimensional figures to solve problems about the planets and the solar system. Also, students use length and proportional relationships to solve problems.

For this activity, students must use the chart of facts and a calculator. Students must use formulas for capacity (Volume = 4/3 * pi * radius3) and area of a sphere (Area = 4 * pi * radius2).

Students should be able to look at the information and create problems similar to those on the activity sheet, especially on the topic of geometry.

For this activity, use the chart of facts below, formulas for capacity and area, and a calculator.

 PLANET Approximate diameter (in miles) Approximate distance from the Sun (in miles) Mercury 3,030 36,300,000 Venus 7,520 67,200,000 Earth 7,930 93,000,000 Mars 4,220 142,000,000 Jupiter 88,900 484,000,000 Saturn 74,900 888,000,000 Uranus 31,800 1,780,000,000 Neptune 30,800 2,800,000,000 Pluto 1,450 3,670,000,000

1. Change each number in the chart to scientific notation.

2. Use the answers from #1 to compute the distance from Pluto to Earth. Show all of your work.

3. How much farther is Neptune from Mercury than Uranus?

4. How many Earths can fit into Jupiter? Show all of your work.

5. If 3/4 of the Earth's surface is water, about how much of Pluto's surface can be covered with Earth's water? Show all of your work.

6. Create a distance or capacity problem of your own using the chart.