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Back-of-the-Envelope Calculations: Volume of the Earth and Sun

Barbara Tewksbury
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Initial Publication Date: May 18, 2005

Summary

Question
Suppose you and your friends wanted to make a scale model of the Earth and the Sun. You start by cutting a one-inch cube of Play-Doh to represent the volume of the Earth.

- How many one-inch Play-Doh cubes would you have to cut in order to represent the volume of the Sun at the same scale?

- If you stacked the blocks up into a cube, how big would the cube be?

- And, finally, if you and all your friends mashed and shaped that huge cube into a sphere, and you made a sphere out of the Earth cube as well, how far away from your Play-Doh Sun would you have to hold your scale Earth to match the true scale of the solar system?

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Assessment

Answer

a) 1.3 million cubes! The volume of the Earth = (4/3)ð’

References and Resources

This SERC page describes the use of Back of the Envelope Calculations

A View from the Back of the Envelope (more info) : This site has a good number of easy simulations and visualizations of back of the envelope calculations.

The Back of the Envelope : This page outlines one of the essays in the book "Programming Pearls" (ISBN 0-201-65788-0). The book is written for computer science faculty and students, but this portion speaks very well to back of the envelope calculations in general.