Lesson 9

Measuring Volume of Solid Objects

Est. Class Sessions: 2–3

Developing the Lesson

Part 2. Measuring the Volume of Solid Objects Using Displacement

The Using Displacement section of the Yolanda Measures Volume by Displacement pages in the Student Activity Book reviews how Yolanda and Josh found the actual volume of a marker using the displacement method. See Content Note.

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Measuring Volume by Displacement. Displacement happens when an object is submerged in a liquid, in this case, water. Measurement of volume occurs when the volume of the liquid displaced is measured. The volume of the immersed object will be exactly the same as the volume of the displaced liquid.

To measure the volume of a solid object, students fill a graduated cylinder with an amount of water that makes it easy for them to calculate the water rise. For instance, if students fill a 250 cc graduated cylinder with 100 cc of water and the water rises to 122 cc when they put the object inside, as in Figure 1, then students can easily subtract 100 from 122 to find the volume, 22 cc.

The object displaces, or pushes aside, its volume in the water, causing the water level to rise. Since the water volume is constant, the new water level can be explained as the volume of the water plus that of the object. To find the volume of the object alone, subtract the starting water level from the final water level.

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Caution students to put the object in the graduated cylinder very carefully so that no water splashes out. They may accomplish this either by gently dropping the object into the graduated cylinder or by tilting the cylinder and letting the object slide in.

After reading this section, assign Question 2. Have students discuss with a partner how Josh found the volume of the marker.

Display the Graduated Cylinders Master and facilitate a class discussion by asking:

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  • Use the display to show how Josh found the volume of the marker. (Possible response: The water level started at 50 cc. Josh slid the marker into the cylinder and the marker pushed the water level up to 62 cc. The marker displaced its volume in the water. 62 cc − 50 cc = 12 cc, and the difference, 12 cc, is the marker's volume.)
  • Do you think this is an accurate measure? Is a volume of 12 cc reasonable? (Yes, because the model of the marker Yolanda built was 14 cc.)
  • What makes 50 cubic centimeters a convenient amount of water to start with? (Possible response: 50 cc is half of the 100 cc graduated cylinder so there is room for the water to rise. It is not too small of an amount and not too great of an amount. 50 is a ten, so it is easy to use in a subtraction problem.)

Tell students if the object floats to push it under the surface of the water and hold it in place until they can read the level of the water. A thin “pusher,” such as the tip of a pencil, a straightened paper clip, or a pin is better to use than a large pusher because the additional volume of a thin pusher will be minimal. If students use a large pusher, such as a finger, their reading for the object's volume will not be accurate.

Ask:

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  • Why is it important that the object be completely under water? (In order to get an accurate measure, the object must be completely under water so that it can displace its total volume in the water.)
  • What else should you do to get an accurate measure? (Read the water level at eye level; use an eyedropper to add the last few drops of water to the cylinder; tilt the cylinder and slide the object in.)

Distribute graduated cylinders, eyedroppers, and containers of water to student groups. Have paper towels available to clean up spills. Students will need the same items that they used in Question 1, when they built models and estimated volume.

Assign Question 3 of Yolanda Measures Volume by Displacement in the Student Activity Book. It directs students to find the actual volume of each object from Question 1, using the displacement method. As you observe students working, check that they are recording the volume of the objects only and not the volume of the water and the objects combined. Figure 2 shows a sample data table with examples of small objects, their estimated volume, and their actual volume.

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Ask students to record the related number sentence for finding the volume of an object using displacement. This trail helps you and students keep track of their thinking while working through a multistep problem.

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Challenge students to find a way to measure the volume of an object that is too big to fit inside a graduated cylinder. One method is to put a container large enough to hold the object inside a pan. Fill the container to the brim with water and place the object inside the container. The object will displace an amount of water equal to its volume. Pour the overflow of water from the pan into a graduated cylinder to measure the object's volume. Another way is to use a graduated cylinder to calibrate a large jar to be used as a graduated cylinder.

Student Guide:
Student Activity Book: 554
Answers
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SG_Mini
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Master:
The rise in the water level after adding a rock
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A sample data table
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