1. Density of an Irregular Solid Object
Water Displacement

2. Let’s Review mass Density = volume
We already know how to calculate the density of any system.
We simply use the density equation or refer to the density pyramid.
Density
mass
volume
Density =
mass
volume

3. To Practice:
A solid object has a mass of 180 grams and a volume of 45 cubic centimeters. What is the density of this object?
Mass = 180 grams
Volume = 45 cubic centimeters

4. Using the “Pyramid”: 4.0 grams/cm3 mass Density = volume 180 grams =

5. But what if the object does not have a nice geometric shape?
height
width
length
How do you find the volume of a solid object that does not have convenient length, width, and height ??
Easy to calculate the volume here !!

6. The answer is: Water Displacement !!!
Fact of Life: A solid object will displace (means pushes out of the way) a volume of water exactly equal to the volume of the object itself. (This will be true for any liquid – not just water…)
Mass of the object has nothing to do with this.
Shape of the object has nothing to do with this.
Only the volume of the object determines how much water is displaced.
This is why the water rises when you get into the bath tub…

7. How does this work? We fill a graduated cylinder half full of water.
This original volume of the water is called the initial volume = Vi
Remember that we read the bottom of the “meniscus” in a graduated cylinder to know the volume of the liquid.

8. Next:
We add the solid object to the graduated cylinder. As expected, the water level rises. The volume of the water after the object has been added is called the final volume = Vf
Remember – this first volume was the initial volume.

9. Now to calculate:
The difference between the initial volume and the final volume is called “delta V”. You can easily determine its value by subtraction. Vf
Δ V
We write “delta V” like this: Vi

10. So…
If an irregular solid object is placed into a graduated cylinder that contains 50.0 ml of water and the water level rises to a final reading of 75.0 ml, we can calculate the Δ V is 75.0 – 50.0 = 25.0 ml.
Vf = ml
ΔV = 75.0mL – 50.0mL
= ml
Vi = ml

11. Here’s the cool part:
It is a “fact of life” in nature that a liquid volume of 1.0 ml is exactly equal to (and therefore interchangeable with) a solid volume of 1.0 cubic centimeter.
So… if the object causes a change in the water volume equal to 25.0 ml, the volume of the object must be exactly 25.0 cm3.
Remember, we describe the volumes of solids in cubic centimeters…

12. Now to connect to density problems:
mass
volume
Remember that density is still equal to mass divided by volume. That equation does not care how you get the volume of the object – it will work for both regular and irregular solid objects.
Δ V is the volume of the object !!