Measuring the Size 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 was selected for the On the Cutting Edge Reviewed Teaching Collection

This activity has received positive reviews in a peer review process involving five review categories. The five categories included in the process are

  • Scientific Accuracy
  • Alignment of Learning Goals, Activities, and Assessments
  • Pedagogic Effectiveness
  • Robustness (usability and dependability of all components)
  • Completeness of the ActivitySheet web page

For more information about the peer review process itself, please see

This page first made public: Jun 30, 2008


In this activity, students explore the method used by Eratosthenes to estimate the circumference of the earth. After engaging with the geometry and data Eratosthenes used, students compute the radius and volume of the Earth.

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

Learning Goals

  • Learn how Eratosthenes used geometry to estimate the circumference of the Earth.
  • Use the circumference to compute the radius and volume of the Earth.

    Mathematical Skills
  • Use the geometry of a circle (radius and circumference) and a sphere (volume).
  • Calculate interior angles.
  • 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 and space 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