The Science Notebook
Exploring Mesurement - Volume

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VOLUME
A Look at English Units of Volume
 Measuring Volume
Metric Units of Volume
More on the Metric Units of Volume
How Much is A Liter?
Making a Measuring Beaker
Using a Graduated Cylinder
Measuring Small Amounts With a Medicine Dropper
Making a Graduated Cylinder


VOLUME

When we measure volume, we measure just how much space something takes up.  Just as with length, our English system of measurement has many different units for volume, everything from ounces to barrels.  The many units used to measure volume in the English system are all different, and they don’t really relate to one another all that well.  We probably don’t give all these different units too much thought because we are so used to using them.  But trying to convert from one unit of measure to another can be a real nightmare! 


A Look at English Units of Volume

Materials Needed: English weights and measures conversion chart (found in many math books, encyclopedias or dictionaries, or online); dictionary.

Procedure:   For each of the following English units, use a conversion chart to find out the number of units in the second column that are equal to one unit in the first column.  You may not be able to find all of these, but find as many as you can.  You may wish to get an older student, teacher, or parent to help you.

Unit of Measure Equals
1 Ounce  _____ Drams
1 Teaspoon  _____ Drams
1 Tablespoon  _____ Teaspoons
1 Cup  _____ Tablespoons
1 Pint  _____ Cups
1 Quart  _____ Pints
1 Gallon  _____ Quarts
1 Peck  _____ Quarts
1 Bushel  _____ Pecks
1 Hogshead  _____ Gallons
1 Barrel  _____ Gallons

What To Look For: There are many different ways to convert from one unit to the next, and there are many more English units that are not shown here.  To make matters worse, some of these units, such as the gallon, are not the same size in all countries.

Going Further: All of the above units were invented because people needed a standard way to measure things.  Often, people just picked a certain amount and set it as the standard.  You can do the same thing. 

Suppose you have five friends and a large bowl of peanuts.  You want to divide the peanuts evenly, but you don’t have any kind of measuring cup, and you certainly don’t want to count out individual peanuts!  So you grab a small paper cup, and start scooping out peanuts for your friends one paper cup at a time.  You have just created your own unit for measuring volume, the peanut cup!  


Measuring Volume


All these units can be confusing, but there is an easier way!  In either the English or the metric system, we can measure volume is by relating it to a standard used to measure length.  In this experiment, we are going to measure the volume of a small box using one of the English units of length, the inch.

Materials Needed: Ruler; shoe box, cereal box, or other small box.

Procedure: Measure the length, width and height of the box to the nearest inch.  Now multiply the length times the width times the height.  Your answer will be the volume of the box expressed in a unit of volume called “cubic inches.” 

What To Look For: Suppose your box was 6 inches high, 5 inches wide, and 9 inches long.  You would multiply 6 times 5 times 9.  Your answer would be 270.  This means that the volume of the box is 270 cubic inches.  Another way of looking at this is that if you had a bunch of blocks that measured one inch on every side, you could fit 270 of those blocks into this box.  A block that is 1 inch on all sides has a volume of 1 cubic inch.
 
What Happened: Don't panic, but you have just used math to figure the volume of a box.  You used something called a “formula” to do this.  The formula used to figure the volume of any box shaped object is “volume equals length times width times height”.  We can use abbreviations to write this formula as follows:

For any box shaped object…

V = L x W x H

...where V = volume, L = length, W = width, and H = height

Try measuring the volume of some other small boxes or box shaped objects.

Going Further: Larger box shaped objects could be measured using other English units.  For example, the volume of your room could be measured by measuring the length, width and height of the room in feet and using the formula above.  The volume would then be measured in cubic feet.  Can you use a yard stick or tape measure to calculate the volume of your room in cubic feet?

The problem is that most objects we want to know the volume of are not box shaped.  If we are going to use cubic inches, feet, yards, or any other unit, we’re going to have to find another way to measure their volume, and we’ll do just that, a little later.  But first, let’s see how the metric system handles volume.


Metric Units of Volume

CAUTION!  Always use sharp objects such as knives or scissors with adult supervision only!  Hold any sharp point away from your body, particularly your eyes.

The metric system does away with all of the different units of volume used in the English system, and instead, uses only one unit to measure volume. That unit is called  the “liter”.  

Materials Needed: Meter stick or metric ruler; stiff cardboard such as poster board; scissors or hobby knife; tape.


Procedure:   Using the meter stick, draw the pattern shown above.  Make sure that each square is 1 decimeter (10 cm) on each side. Now cut out the pattern on the solid lines and fold along the dotted lines to make a box that is 1 dm (abbreviation for “decimeter”) on each side.  Tape the sides as shown. Save this box for the next experiment.


What To Look For: Since we know that the length of each side is 1 decimeter, using the formula from the previous experiment, we can calculate the volume of this box using the formula we just learned:

V = L x W x H

so...

V = 1 x 1 x 1 = 1 cubic decimeter.

What Happened:  The metric system defines 1 cubic decimeter as 1 liter, so the volume inside this box is equal to 1 liter.  Most smaller volumes may be measured in liters, or in portions of a liter, as we will see.


More on Metric Units of Volume

Materials Needed: The box from the last experiment; a ruler that measures centimeters.

Procedure:   Measure each side of the box in centimeters.  Use the formula for the volume of a box shaped object (V = L x W x H ) to calculate the volume of this box in cubic centimeters.

What Happened: Each side was 10 cm long.  When you plug the numbers into the formula and do the math, you get:

V = L x W x H

V= 10 x 10 x 10 = 1000 cubic centimeters


This means that 1 liter also equals 1000 cubic centimeters.  Since the size of the box did not change, it also means that 1000 cubic centimeters equals 1 cubic decimeter.


How Much Is A Liter?

Now that we know how the liter came about, we need to get some idea of just how much a liter is.

Materials Needed: A container that will measure one liter; a container that will measure one quart; box from the last two experiments; plastic food wrap or plastic bag (such as a grocery bag; water.

Procedure:   Many home measuring cups that hold two cups will also have a metric scale. On the metric scale you should see a ½ liter mark.  Obviously, two of these would equal 1 liter.  If you don’t have such a measuring cup at home, borrow a container from your school science lab that measures 1 liter.  Your teacher can help you with this.  If you can find a quart jar used for home canning, this will be marked to measure 1 quart, and it may even have a metric scale that shows 1 liter as well.

Using your measuring device, measure out one liter of water.  Pour this water into the quart container. Notice how much water is in the jar.  Is it more or less than a quart?

Place the plastic wrap or bag inside the cardboard box.  Make sure that there are no holes in the plastic and fit the plastic as near to the edge as possible.  Measure another liter of water and carefully pour this water into the box.  Does it just fill the box?
 
What Happened: When you poured the liter of water into the quart jar, you saw that a liter is just a little more than a quart. Also, if you measured carefully, you saw that your 1 cubic decimeter box held exactly 1 liter.  This proves what you learned in the last experiment: 1 liter equals 1 cubic decimeter or 1000 cubic centimeters.


Making a Measuring Beaker


An important piece of lab equipment is a beaker used for measuring liquids.  From time to time you will find it useful to have such a beaker for your experiments.  By working carefully, you can make a measuring beaker for almost nothing that will be every bit as good for your purposes as one you could buy.  It will also help you to understand how the liter is used as a standard of measurement.

Materials Needed: Clear plastic jar such as a peanut butter jar; a measuring beaker (borrowed from school) or a measuring cup graduated in milliliters (ml); a waterproof marking pen; masking or duct tape; waterproof pen.

Procedure: A liter may be divided into 1000 equal parts.  Each part is called 1 milliliter and is abbreviated 1 ml.  A liter may also be divided into 100 equal parts (centiliters), or 10 equal parts (deciliters).  (If you checked out the Measuring Length page. you’ve seen these prefixes before.)  However, for almost all measuring of small amounts, milliliters are used, and that’s what you’ll use to make the scale for your measuring cup.

You should find a jar that has smooth straight sides if at all possible.  Although you can use a jar that doesn’t have smooth sides, one with straight sides will be easier to read.  Place a strip of tape along the side of the jar from top to bottom.  Using the measuring beaker or measuring cup, measure out the smallest amount shown on the markings for the beaker or cup (probably 50 ml) and pour the water into your jar.  Carefully make a mark on the edge of the tape that is exactly even with the level of the water as shown.  Repeat this process until the jar is almost full.  A typical “family size” peanut butter jar may hold about 500 ml, but yours may hold more or less, depending on the size.

Now go back and mark the amounts on the tape.  If your marks are close together, you may only want to place the amount beside every other mark.  For example, if each mark was 50 millimeters, you might not write anything beside the 50 ml mark, but would write 100 ml beside the second mark, 200 ml beside the fourth mark, and so on.  It all depends on how much room you have and how much your container holds.  If you have a steady hand, you may make your marks directly on the plastic instead of using tape.  This will make the beaker much easier to clean, and you won’t have to worry about the tape coming off if it gets wet.

The process of using a known standard to create another measuring device is called “calibration”.  Any measuring device you make will have to be compared to a known standard (in this case the measuring cup or graduated beaker) to make sure that it accurately measures what you want it to measure.  You have just calibrated your measuring beaker by using the measuring cup or the beaker from school.


Using a Graduated Cylinder



A graduated cylinder is a tall glass or plastic cylinder which is used to accurately measure small amounts of liquids.  It is much more accurate than a measuring beaker, and is therefore, usually more expensive.  While you can buy smaller and relatively inexpensive graduated cylinders at many school supply stores, it isn’t likely that you would want to buy one for you home laboratory.  However, if you find the right container, a graduated cylinder is fairly easy to make as you will soon see, but you will need to borrow a graduated cylinder to calibrate your homemade one.

Before you make your own graduated cylinder, you will first need to learn how to use one properly.

Materials Needed: Graduated cylinder; water; medicine dropper.

Procedure: Borrow a graduated cylinder from your school, or use one there during your free time.  Look at it carefully.  You will notice that it has a series of lines that go all the way around the cylinder.  These lines are called graduations.  That is how this device gets the name “graduated cylinder”. 

On most cylinders, each line equals 1 milliliter, but if you aren’t sure, ask your teacher.  Once you know how the cylinder is marked (or graduated), reading it is easy.  It is just like a measuring cup except for one thing. 

Add some water to the cylinder and bring your eye level even with the surface of the water.  If you look carefully, you will see that the surface of the water curves up slightly along the edges and down in the middle.  The edge of the surface can be as much as a milliliter above the bottom.  These cylinders are made so that when you observe the water level, you should read the line nearest to lowest level of the water. 


Now practice measuring different amounts of water until you get the hang of it.   First, just add different amounts to the cylinder and read how much is there.  Do this four or five times.  Then, measure out the following amounts: 5 ml, 8 ml, 17 ml, and 34 ml.  You may want to have your teacher or an older student check behind you. You may also want to use a small medicine dropper to help you add or remove small amounts of water.


Measuring Small Amounts With a Medicine Dropper

Materials Needed: Small container of water; medicine dropper or plastic pipette; graduated cylinder; paper and pencil.

Procedure:   Take up some water in the medicine dropper or pipette.  Carefully begin adding water to the graduated cylinder, drop by drop, counting the drops as you go, until you get exactly 5 milliliters (ml). Remember to read from the bottom of the water level!  Write the number of drops required to do this. Divide the total number of drops by 5 to get the number of drops in 1 ml.   Write this number down so you can refer back to it later! This is a useful way to measure small amounts of liquid, so save this dropper or pipette to use later.  (You need to always use the same dropper or pipette because the size of the drops from a different one may be larger or smaller.)

Going Further: You may be wondering why you just didn’t count the number of drops in 1 ml.  You could do that, but sometimes, when you are dealing with very small amounts, your measurement will be more accurate if you measure out a larger amount and then divide as you did here.  Do you know why?


Making a Graduated Cylinder



Materials Needed: Translucent or clear 35 mm film canister or plastic medicine bottle; graduated cylinder (borrowed from school); water; fine tip permanent marker or pencil; duct tape or masking tape.

Procedure: The container you choose should allow you to see water from the outside.  If you are to accurately measure milliliters, the sides of the container must also be straight. Place a strip of tape from top to bottom on the outside of the container.  Using the graduated cylinder, measure out 5 ml of water and pour it into the container.  Draw a thin line on the tape. The top of the line should be even with the surface of the water.  Repeat this process until the bottle is almost full.  Number each mark 5, 10, 15 and so on.

Then, using a ruler, divide the spaces between each mark into 5 equal parts.  Each mark will represent 1 ml. If you have a steady hand and you are using a permanent marker, you can eliminate the tape and make your marks directly on the container.  Your graduated cylinder is now ready to use. 

Going Further: By making the measuring beaker and the graduated cylinder, you have learned the basic principle behind making many useful measuring devices.  You can now use your imagination and whatever you have on hand to make any other measuring containers you might need.


Understanding how to measure volume is a useful tool in science,  Measurement is so important in science that you should check out our page on Measuring Length if you haven't already done so, as well as our page on Measuring Mass.


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