Why does a jar full of water have a larger mass than an identical jar full of air? Watch this video to learn about how mass and volume are used to calculate density.
Lesson A8: Density
Figure A.3.8.1 – An ancient Greek king asked the scientist Archimedes to figure out if his crown was pure gold.
Figure A.3.8.2 – Archimedes figured out the answer to the king’s problem while taking a bath.
Archimedes’ Bath
Archimedes was a Greek scientist and mathematician who lived 2200 years ago. A famous story about Archimedes involves volume and density. A king asked Archimedes to figure out if his crown was pure gold or not. Archimedes needed to figure out the
density of the crown without damaging it. How did he solve this problem? Legend says Archimedes yelled “Eureka” when he found the answer.
Reading and Materials for This Lesson
Science in Action 8
Reading: Pages 32–37
Materials:
No additional materials are needed for this lesson.
Watch More
Eureka!
Watch this video to learn how Archimedes determined the density of the king’s crown.
Figure A.3.8.3 – Plastic wrap is made from low density polyethylene (LDPE) plastic.
Figure A.3.8.4 – Many plastic bottles are made from high density polyethylene (HDPE) plastic.
Figure A.3.8.5 – A recycling code of "2" is found on HDPE plastics. LDPE plastics have a code of "4".
Low Density Polyethylene Plastics
Modern humans use plastics everyday for many purposes. We use plastics to store and transport food and cosmetics. Vehicles and electronics contain many plastic parts. Our homes are filled with plastics.
Plastics were invented approximately 100 years ago. The majority of plastics are made from crude oil. One reason that plastics are so useful is because they have a relatively low density. This makes plastics useful as containers. Before the invention
of plastics, containers were often made from glass or metal. Glass and metal are more dense than plastic, which makes them heavier. Less dense plastic containers require less energy and less money to transport.
Low density polyethylene, or LDPE, is a type of plastic with a very low density. LDPE is used to make very lightweight plastic films, like Saran Wrap™ or flexible squeeze bottles.
High density polyethylene plastic, or HDPE, has a higher density than LDPE, but still has a relatively low density. HDPE is strong, so it is often used to make plastic bottles for fluids.
Watch More
LDPE and HDPE Plastics
This video explains more about LDPE plastics.
Watch this video to learn more about HDPE plastics.
Connections
Figure A.3.8.6 – The volume of regular prisms can be found by multiplying the length x width x height.
Connections – Math >> Volume and Density Calculations
In order to figure out an object’s density, you need to know its mass and volume. The density of an object can be determined by dividing its mass by its volume:
The mass of an object can easily be measured with a scale. The volume of an object can be measured by two different methods. As Archimedes discovered, an irregular shaped object will displace its volume of water.
Some objects have regular shapes. It is possible to calculate the volume of a regular shape without immersing it in water. The volume of a box can easily be found by multiplying its length, its width, and its height.
For example, if you had a 200 g box with a length of 10 cm, a width of 2 cm, and a height of 5 cm, what is its density?
You would multiply 10 cm x 2 cm x 5 cm to determine the box’s volume of 100 cm3.
If you need to review how to calculate density, watch the lesson video again. Then, try finding solutions to these questions:
A box of baking soda has a mass of 454 g. This is the weight of the baking soda on its own, not including the box. The box has a height of 12.1 cm, a length of 8.90 cm, and a width of 5.00 cm. What is the density of baking soda?
This is a challenge question to stretch your brain!
You have a bag of sugar that has dimensions of 10.3 cm by 12.9 cm by 7.10 cm. You don’t have a scale, but when you search online, you find that the density of sugar is 1.59 g/mL. What is the mass of the sugar in kilograms?
Figure A.3.8.7 – Compare the densities of (from left to right) charcoal, an egg, gold, iron, and oak wood.
Determining Density
Problem:
How do the densities of five different materials compare with each other?
In this virtual experiment (click on the Virtual Density Lab, then click on Open in a New Window), you will measure the mass and volume of five different objects and determine their densities. This experiment uses Archimedes’ discovery of finding an object’s volume by its displacement of water.
Hypothesis:
A
hypothesis is a testable answer to a scientific question. In other
words, what do you think the result of this activity will be?
Hint: The five objects are charcoal, egg, gold, iron, and oak wood.
Which object do you think will have the highest density? Why?
Which object do you think will have the lowest density? Why?
Download & Website:
DOWNLOAD this document. It
provides a space for you to write your own hypothesis. Also use the document to write your observations and analysis questions that come later in this activity.
Go to the website http://ippex.pppl.gov/interactive/. Click on the link for the "Virtual Density Lab".
Click on the "Open in a new window" link.
Instructions:
For the liquid choice, click on water.
Drag each object to the scale. Measure the mass of each object and record these masses on your observations table.
Drop each object into the graduated cylinder. Note the volume of water that each object displaces. Record these volumes on your observations table.
Calculate the density of each object and record these densities in the observations table.
Observations:
Object
Mass (g)
Volume (mL)
Density (g/mL)
Charcoal
Egg
Gold
Iron
Oak wood
Questions:
Think about the following questions very carefully. Refer to your observation table. Then, type or write your answers. When you have your answers, click the questions for feedback.
The objects in order from highest to lowest density are gold, iron, egg, wood, and charcoal.
Try It!
Comparing Baking Soda and Honey
The mass and volume of baking soda and honey samples were measured and recorded. Use the following table with experimental data to calculate the density of baking soda and honey.
Download:
DOWNLOAD this document.It includes the following table of experimental data where you can record your the densities that you calculate. Also use the download to write your analysis questions that come later in this activity. At the end of the download document, you will
also find an answer key for the density calculations. Do not look at the key until you have done the density calculations yourself!
Instructions and Experimental Data:
Use the provided data for baking soda and honey to calculate density. Because there are four measurements for each substance, you need to do four density calculations for each substance.
Mass and Volume of Baking Soda
Mass (g)
Volume (mL)
Density (g/mL)
225
100
435
200
660
300
900
400
Mass and Volume of Honey
Mass (g)
Volume (mL)
Density (g/mL)
142
100
280
200
415
300
564
400
Compare your density calculations to the key at the end of the document you downloaded.
Questions:
Think about the following questions very carefully. Then, type or write your answers in the document you downloaded. When you have your answers, click the questions below for feedback.
As the mass and volume of the baking soda increased, its density stayed the same. As the mass and volume of the honey increased, its density stayed the same.
When people take experimental mass measurements, they might be reading a scale that is not 100% precise. This would result in mass measurements, and density calculations that are slightly lower or higher than the actual density.
Changing the mass and the volume of a substance does not change its density. The particles of a substance have the same mass and spread out in the same way, regardless of the amount of substance present.
Sharing:
Congratulations on completing this activity! Consider sharing your completed work (or any thoughts and experiences you might have regarding this activity) in the course Sharing Forum.
You can also email your completed work to your teacher and ask for feedback.
Make sure you have understood everything in this lesson. Use the Self-Check below, and the Self-Check & Lesson Review Tips to guide your
learning.
Unit A Lesson 8 Self-Check
Instructions
Complete the following 6 steps.
Don't skip steps – if you do them in order, you will confirm your
understanding of this lesson and create a study bank for the future.
ANSWER all the questions on the downloaded quiz in the spaces provided. Think carefully before typing your answers. Review this lesson if you need to. Save your quiz when you are done.
COMPARE your answers with the suggested "Self-Check Quiz Answers" below. WAIT! You didn't skip step 2, did you? It's very important to carefully write out your own answers before checking the suggested answers.
REVISE your quiz answers if you need to. If you answered all the questions correctly, you can skip this step. Revise means to change, fix, and add extra notes if you need to. This quiz is NOT FOR MARKS, so it is perfectly OK to correct
any mistakes you made. This will make your self-check quiz an excellent study tool you can use later.
SAVE your quiz to a folder on your computer, or to your Private Files. That way you will know where it is for later studying.
CHECK with your teacher if you need to. If after completing all these steps you are still not sure about the questions or your answers, you should ask for more feedback from your teacher. To do this, post in the Course Questions Forum,
or send your teacher an email. In either case, attach your completed quiz and ask; "Can you look at this quiz and give me some feedback please?" They will be happy to help you!
Be a Self-Check
Superhero!
Self-Check Quiz Answers
Click each of the suggested answers below, and carefully compare your answers to the suggested answers.
If you have not done the quiz yet – STOP – and go back to step 1 above. Do not look at the answers without first trying the questions.
Both bags have the same density because they contain the same substance, which is sugar. If both bags have the same density, the 1 kg bag must have a smaller volume than the 5 kg bag.
The volume of the iron nail is equal to the volume of the displaced water in the graduated cylinder. Taking the difference of the graduated cylinder readings, 12.0 minus 9.0, the volume of displaced water equals 3.0 mL. Thus, the volume of the
iron nail is 3.0 mL. Density is equal to mass divided by volume, so a mass of 23.4 g divided by 3.0 mL equals 7.8 g/mL.
The volume of the glass cube is 4.00 cm x 4.00 cm x 4.00 cm, which is equal to 64.0 cm3 or 64.0 mL. Density is equal to mass divided by volume, so a mass of 153.6 g divided by 64.0 mL is equal to 2.40 g/mL.
Reading and Materials for This Lesson
