Mass and Density of the Earth

Kéyah Math Project development team: Nancy Zumoff, Christopher Schaufele, Steven Semken, Tracy Perkins, Lynn Onken, Philippe Laval, David Gonzales, and Andrew Becenti (deceased).
Kéyah Math Project directed by Steven Semken , Arizona State University; and Christopher Schaufele and Nancy Zumoff, Professors of Mathematics, Emeritus.
Archived at Arizona State University School of Earth and Space Exploration.


This activity is intended as a follow-up to the Measuring the Size of the Earth and Measuring the Size of the Earth from Arizona activities. Students use data on the radius and volume of Earth, Newton's Law of Gravitational Attraction, and density equations to compute the mass and density of Earth.

Click here to view the full activity on the Kéyah Math Project website.

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Learning Goals

  • Use estimates of the radius and volume of the Earth from other Kéyah Math activities {link} to compute its mass and density.
  • Apply Newton's Law of Gravitational Attraction and density equations.

    Mathematical Skills
  • Use the geometry of a circle (radius and circumference) and a sphere (volume).
  • Calculate interior angles.
  • Apply formulas for force and density.
  • Solve equations involving kinetic energy, mass, and volume.
  • Context for Use

    This activity consists of a set of quantitative problem-solving exercises that can be used as an in-class activity or an assignment in any introductory geology, geography, or Earth science course.

    Description and Teaching Materials

    Teaching Notes and Tips

    An Instructor's Guide to all Kéyah Math activities is available online from the Instructor Resources page on the Kéyah Math website.


    Students record their work and answers in a word-processor document or a notebook, which can be submitted to the instructor for assessment. Solutions to these problems are available online from the Instructor Resources page on the Kéyah Math website.

    References and Resources