10182

# The Principle of Archimedes

A gold sphere is submerged in water. It is suspected that the center might be empty or made of some lighter material. According to Archimedes's principle, we can determine the volume of the inner sphere by measuring the difference between the weight of the entire sphere in and out of water; that difference must be equal to the buoyant force, the weight of the volume of water displaced. Then the difference between the volume of gold in the hollowed sphere and the volume of the water displaced equals the volume of the inner sphere.
This experiment supposedly originates in a problem solved by Archimedes, who was asked by the king if the royal crown was made of pure gold. According to the traditional account, the solution occurred to him in a eureka moment in the bath.
The density of water is and the density of gold is . The weight of the solid gold sphere is equal to . The volume of water displaced is . The buoyant force is .

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.