# Size, Mass, and Density of the Earth

## Summary

This activity combines the exercises from several Kéyah Math activities in guiding students to use the mathematics of Eratosthenes and Newton with actual data, in order to compute the size, mass, and density of Earth.

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

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## Learning Goals

Objectives
• Learn how Eratosthenes used geometry to estimate the circumference of the Earth.
• Use the circumference to compute the radius and volume of the Earth.
• Use these data to compute the mass and density of Earth.
• 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.

## 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.

## Assessment

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.

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