# Back-of-the-Envelope Calculations: Weight of Gold

**This activity was selected for the On the Cutting Edge Exemplary Teaching Collection**

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This page first made public: May 18, 2005

#### Summary

*Question*

Let's suppose that you have a shoe box full of water (the box is waterproof, of course). The shoe box weighs about 9 kg (19.8 pounds). Suppose you emptied the box and filled it completely with rock (little or no air space). How much would it weigh? Let's empty the box again and fill it completely with pure gold. How much would the box weigh now?

## Assessment

*Answer*

Full of rock, the box would weigh about 24 kg (about 53 pounds. Full of gold, the shoe box would weigh 171 kg (about 376 pounds!). Water has a density of 1 gm/cm3. An average rock has a density of about 2.7 gm/cm3, so filling the box with rock would make every cubic centimeter weigh 2.7 times what it does if it were filled with water (in this case 24 kg). Gold, on the other hand, has a density of 19 gm/cm3, or 19 times that of water. If your shoe box were full of gold, it would weigh 19 times what it would if it were full of water. Kind of puts into perspective those movies with people lugging around chests full of pirate gold doesn't it!

## 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 site may be offline. ) : 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.