Name: ____________________________ Homeroom: _____
SCI 8: Fluids
SCI 8: Archimedes’ Principle of Displacement: An Investigation
Curriculum Outcomes Addressed
• Analyze quantitatively the density of various substances and suggest explanations for discrepancies in data, such as the measurement of the
volume of irregular objects by water displacement (210-7, 307-11)

Displacement: “The removal of something by something else that takes its place.”

Archimedes’ Principle: “The volume of the fluid displaced by a sunken object equals the volume of
that object; also, the mass of the fluid that is displaced by that object is
equal to the buoyant force that is acting on that object.”

Density: “The mass of a substance (number of particles of substance) per unit volume.”

Volume: “The amount of space occupied by the matter of a substance.”

Mass: “The amount of matter in a given volume of a substance.”
In order to calculate the density of an object, we have to know the object’s mass and the object’s volume.
Density = _Mass_
Volume
It is easy to figure out the mass of an object – we can place it on a scale and read its mass.
It is also easy to measure the volume of regular objects such as squares/cubes, rectangles, triangles, and
spheres, because we can use simple formulas to calculate it if we know such as these:
Cube (Square)
Volume
Formula
Sphere (Circle)
V = length x width x height
Triangle
V = (1/3) base x height
** r = radius, ∏ = 3.1415
Calculating the volume of irregular objects however, can be tricky. As we have seen in the video, Archimedes
accidentally discovered that the principle of displacement could be used to measure the volume of irregular
objects. He found that the volume of the fluid displaced by a sunken object equals the volume of that object.
Once Archimedes found the volume of the crown by the principle of displacement, and because he was able to
weigh each crown for their masses, he was able to calculate the density of both crowns – the density of the
King’s crown was lower than that of the pure gold crown, which proved to Archimedes that the King’s crown
was not made of pure gold.
Kluge2012
Name: ____________________________ Homeroom: _____
SCI 8: Fluids
Let’s Investigate Archimedes’ Principle of Displacement
We are going to investigate Archimedes’ principle of displacement as a class. Make sure to following along with this
investigation and record all of the necessary components and measurements as we move through this investigation.
1. Record the masses of all objects in the table below.
2. Calculate the volume for each of the objects, and then record them in the table below.
3. Calculate the densities of each of the objects using the density formula, and record in the table below.
Cube 1
(large)
Cube 2
(small)
Sphere 1
(large)
Sphere 2
(small)
Crown 1
Crown 2
Mass
Volume
Formula
Volume
Density
4. How did finding the volume differ between the regular objects (cubes and spheres) and the irregular
objects (crowns)? Briefly explain what you had to do to find the volume of each:
Regular objects:
Irregular objects:
5. A) Compare the densities of the objects in the table. Is there a trend? Explain.
B) Are there any objects that do not follow this trend? If so, which object is this, and why?
6. What are two sources of error that you think could have affected the outcome of our results?
1)
2)
Kluge2012