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Egg Volume Relay

This game recreates Archimedes' "Eureka!" moment, without having to take a bath. Students participate in a relay race that tests their speed and skill in measuring the water displaced by an egg.

The Story:
Archimedes was asked by a king to figure out whether the king's crown was pure gold or gold mixed with silver. Archimedes knew that he had to figure out the crown's density: how heavy it is compared to how much space it takes up (which is mass divided by its volume). It was easy enough to figure out how heavy it was but its volume was tricky.

Archimedes went off to think about this in a nice hot bath. While he was in the bath he noticed that the more of himself he put under water, the higher the water level rose. He realized that the amount of water that rose was equal to his own volume. He was (supposedly) so happy to make this discovery that he ran out into the streets naked shouting "I found it!" ("Eureka!").

Archimedes had found an easy way to measure the volume of an irregularly shaped object. If you submerge the object in water, it will displace a volume of water equal to its own volume. He could use this method to find the volume, and thus the density of the crown. Legend has it that he was able to compare the crown's density to the density of gold, and thus show that the metal in the crown wasn't pure.

Our Eggsperiment:
When we fill up a glass with water, put an egg in the glass and measure the water that rises up (or spills out), we discover the volume of the egg.

Here's an example of the method used in this activity:

Imagine 20 ml of water in a cylinder. Put an object into the water you will see how the level of water in the cylinder has moved up (to 23 ml, for example). The volume of displacement is how much the water level has changed (in this case, it is 0.3 ml). The volume of the object is equal to this amount because it is the amount of space that it took up while in the water. In other words, the volume of the displaced water is equal to the volume of the object.

Objectives

  • Measure the density of an egg using water displacement.

Materials

  • Per Group of 4 students:
    1 egg (plus a few extra)
    1 pencil
    4 half-sheets of scrap paper
    a large graduated measuring cup (with graduated measurements on the glass) or a graduated cylinder wide enough to get an egg in and out
    a bucket or bowl to catch the possible water overflow

Key Questions

  • Why does the rise in water level tell us the volume of the egg?
  • Why was the goal to measure within 10 ml of each other? Why would the measurements not all be identical?
  • Why do we write the second number above the first one rather than the other way around?

What To Do

Preparation

  1. Set up 1 measuring station per group.
  2. Each station should have one bucket/bowl containing a graduated measuring cup that has enough water to cover the egg completely, along with 1 pencil and 4 scrap sheets of paper.
  3. Designate the “starting place” for each team. The stations and starting places should be arranged around the classroom, or outside if water spillage is a concern, in a way that the students from opposing teams will not bump into each other while running back and forth.

Game

  1. Divide the students into teams of 4. Assign a station for each team.
  2. Give each team 1 egg, 4 pencils and 4 sheets of paper.
  3. This is a relay race. The first person will run with the egg to their measuring station, write down the water level, add their egg, write down the new water level, and subtract one from the other. This will give the amount of water displaced by your egg.
  4. Once you have your answer, place the sheet of paper upside down next to your station.
  5. Run back to your team and pass off the egg to the next team member.
  6. The next team member takes the egg and repeats the same measurement drill.
  7. Repeat the process 2 more times with the remaining teammates.
  8. Each team has 4 members so each egg will get 4 measurements.
  9. The winning team will be the fastest one that also has 4 measurements within 10 ml of each other (adjust the 10 mL allowance depending on the equipment and skill of your students).

Teacher Tip: If your students struggle with subtraction, help them out by printing this grid onto the sheets of paper

Extensions

  • Introduce the term ‘displacement’. Displacement occurs when an object is immersed in a fluid, pushing it out of the way and taking its place. The volume of the fluid displaced can then be measured. The volume of the immersed object will be exactly equal to the volume of the displaced fluid.
  • Find the volume of other objects in the classroom (for objects where water damage is not an issue).
  • In SI (International System) units, density is equal to the mass in kg divided by the volume in cm3 or ml. As an extension for older students, you can have them calculate the egg’s density by dividing its mass (kg) by its volume (ml), as determined by this activity.