1. How to Solve Density Problems using the D.U.F.A.S. method
Earth/Physical Science
Mr. Woodruff

2. Physical Properties
Physical property is a property that can be observed without changing the identity of the substance.
Examples:
viscosity
conductivity
malleability
hardness
magnetism
melting point
boiling point
density
color

3. The D.U.F.A.S. method “Don’t be a dummy, use D.U.F.A.S.!”
Data - what do you know from the problem? What is the unknown you are solving for?
Units – What are the units of the data given? Does every number have a unit?
Formula- What is the formula you need to use to solve your problem?
Arrange- Plug in your data to the formula
Solve - crank up your calculator and get the answer

4. The Formula for Density
Density is equal to the Mass of the object divided by the Volume of the object.
D=m/v
Power Triangles for
Density m or
mass D v xx x
Density
volume

5. How do you figure out Mass?
Place your object on the weighing pan of a metric scale.
Read and record the object’s mass in grams or
Zero out a triple beam balance and then place the object on the weighing pan.
Slide the weight tabs on the beams until the indicator is balanced again. Add the total masses and record the total.

6. How do you calculate Volume
If you have a regular shaped object, measure the object’s width, height, and length in centimeters. Multiply the three lengths together and record the value.
L x W x H = Volume
If the object is irregular in shape use the Water Displacement Method.
Put the object in a beaker with a measured level of water. Record the new level after you place it in the beaker. Subtract the old initial measure (Vi) from new final measure (Vf) and you have the object’s volume in mL or cm3. Vf – Vi = V (object)

7. Select the formula
Use the power triangle. Cover the unknown, what’s is visible is the formula.
In our examples:
to solve for D use: D= m/v
to solve for m use: m= D x v
to solve for V use: V = m/D
The right Formula gets the right answer !!

8. Does every number have a Unit?
What are the Units?
Mass is measured in g
Volume is measured in cm3 or mL
Density is measured in g/cm3 or g/mL
Does every number have a Unit?

9. Get the Data from the problem: Mass, Volume & Density type
What is the density of a brick measuring cm x 15 cm x 20 cm massing 6000g.?
Density = ? g/cm3
Mass = 6000g
Volume = 10cm x 15 cm x 20 cm = 3000 cm3
Density = m/v = 6000g/ 3000 cm3
Density = 2 g/cm3

10. Mass, Volume& Density problem
What is the mass of a block of granite that has density of 5 g/cm3 and volume of 40 cm3?
Mass Formula is m= D x v
Arrange the data in the formula:
?g = 5g/cm3 x 40cm3
Solve the equation:
?g = 5g/cm3 x 40cm3 = 200g
The granite has a mass of 200g.

11. Get the Data from the problem: Mass, Density & Volume type
What is the volume of a 900 gram chunk of lead with a density of 15 g/cm3?
Volume = ?cm3
Mass = 900 g
Density = 15 g/cm
Formula for Volume is V= m/D Volume equals mass divided by Density
Arrange ?cm3 = 900 g / 15 g/cm3 = 60 cm3
The volume of the chunk of lead is 60 cm3

12. Density is an intrinsic Physical Property
The density of a substance is unchanging as long as the substance does not change.
A lump of gold has a density of 19.3 g/cm3. If you cut the lump in half, the density of the gold is still g/cm3. The mass and volume of the “half lumps” would be half the original mass and volume; but the density would still be 19.3 g/cm3.

13. “See how it’s done” problems
Don’t be a dummy!
Use D.U.F.A.S.
Data
Units
Formula
Arrange
Solution

14. D. U. F. A. S. Formula for Density: D= m/v m= v = D = 70.0 g 20.0 cm3
What is the density of a piece of iron that has a mass of 70.0g and a volume of 20.0 cm3
Data Table & Units
Formula for Density:
D= m/v m=
v =
D =
70.0 g
20.0 cm3
? g/cm3
Arrange:
? g/cm3 = 70g/20 cm3
Solution:
D= 3.5 g/cm3 D. U. F. A. S.

15. D.U.F.A.S. D.U.F.A.S. m= v = D = 125.0 g ? cm3 . 500 g/cm3
I threw a plastic ball in the pool for my dog to fetch. The mass of the ball was 125 grams. What must the volume be to have a density of g/cm3 ( I want it to float of course!)
Data Table & Units
Formula for Volume:
V=m/D m=
v =
D =
125.0 g
? cm3
. 500 g/cm3
Arrange:
? cm3 = 125g/.500 g/cm3
Solution:
v= 250 cm3
D.U.F.A.S.
D.U.F.A.S.

16. D.U.F.A.S. D.U.F.A.S. Formula for Mass: m= D x v Arrange:
A block of aluminum occupies a volume of 15.0 cm3 and density of 3.0 g/cm3? What is its’ mass?
Formula for Mass:
m= D x v
Data Table
& Units m=
v =
D =
? g
15.0 cm3
3.0 g/cm3
Arrange:
? g = 15.0 g/cm3 x 3.0 cm3
Solution:
The aluminum’s mass is 45.0 g
D.U.F.A.S.
D.U.F.A.S.