Measurement measuring volume, Summaries of Physics

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J. Clark,

Measurement measuring volume

Student Exploration: Measuring Volume

Vocabulary: cubic centimeter, diameter, graduated cylinder, meniscus, milliliter, pipette, radius, rectangular prism, sphere, volume, water displacement Prior Knowledge Question (Do this BEFORE using the Gizmo.) Albert plays football. His sister Juliana plays volleyball. While walking home from practice one day, Albert and Juliana argue about which is bigger, a football or volleyball. How would you measure and compare the sizes of the two balls? I’d compare them based on how they look. You can also compare them by finding out their volumes and comparing them. Gizmo Warm-up When scientists talk about how big something is, they are really talking about its volume , or the amount of space it takes up. The Measuring Volume Gizmo allows you to measure the volumes of liquids and solids using a variety of tools. To begin, remove the 50 - mL graduated cylinder from the cabinet and place it below the faucet. To turn on the faucet, drag the slider next to the faucet up. Fill the cylinder about halfway, as shown.

1. Place the magnifier over the waterline. Draw a sketch of what you see in the area at right. Label the large tick marks on your sketch. What volume is represented by each small tick mark? 1 mL
2. What is the shape of the waterline? The waterline is curvy. This curved shape is called the meniscus. Always read the volume at the bottom of the meniscus.
3. What is the volume of water in the graduated cylinder? 25 mL (definitions on last page)

Activity A (continued from previous page)

5. Practice: Use the Gizmo to complete each of the following challenges. When you have finished each one, take a screen shot and add it to your document. Label each image with the volume. A. Fill the 25 - mL graduated cylinder with 11.5 mL of water. B. Fill the 100 - mL graduated cylinder with 76.0 mL of water. C. Fill the 50 - mL graduated cylinder with 38.5 mL of water.
6. Think and discuss: Suppose you needed to measure exactly 15.0 mL of water for an experiment. Which graduated cylinder would be the best one to use, and why? The 25 mL cylinder would be the best one to use when measuring exactly 15 mL because that cylinder has 15 mL labeled.
7. Further practice: Select the Practice button. In this mode, the Gizmo will give you a series of challenges. When you complete a challenge, click Submit. Click Reset if you would like to start over or try a problem again. As you practice, the Gizmo will keep a tally of right and wrong answers in the green and red circles. Complete the first six challenges. Stop when you see the ruler and sphere (ball) on the screen.

Activity B: Regular solids Get the Gizmo ready:

• Select the Free Exploration mode.
• Return all items to the cabinet.
• Drag the block and the ruler to the counter.
• You will need a calculator for this activity. Introduction: The volumes of regular solids, such as spheres (balls) and rectangular prisms (blocks), can be determined by measuring their dimensions. The volume of a solid is usually expressed in cubic centimeters (cm^3 ). One cubic centimeter is exactly the same volume as 1 milliliter. Goal: Measure and calculate the volume of a rectangular prism and a sphere.

1. Observe: Count the squares in the rectangle at right to find its area. A. What is the area of the rectangle? 8 cm B. How does the area of the rectangle relate to the lengths of each side? Area equals length times width.
2. Observe: A block is an example of a rectangular prism. A rectangular prism has six rectangular faces. Look at the block shown below. Each cube inside the block has a 1 - cm side and a volume of 1 cm^3 , or 1 mL. A. What are the length, width, and height of the block? Length: 3 cm Width: 3 cm Height: 4 cm B. Multiply these three dimensions. What is the product of the length, width, and height? 36 C. How many cubic centimeters are in the block? 66
3. Measure: Just as the area of a rectangle is the product of its length and width, the volume of a rectangular prism is equal to the product of its length, width, and height. In the Gizmo, place the ruler over the block. A. What are the length, width, and height of the block? Length: 4.18 Width: 2.67 Height: 7. B. What is the volume of the block? 85.2 cm (Write your answer to the nearest 0.1.) (Activity B continued on next page)

Activity C: Water displacement Get the Gizmo ready:

• Select Free Exploration.
• Return all objects to the cabinet.
• Drag the large sphere , the overflow cup , the 250 - mL beaker , the 50 - mL graduated cylinder , and the magnifier to the counter. Introduction: Have you ever climbed into a tub and seen the water rise? The amount the water rises is related to your size—the bigger you are, the more the water will rise. This method, called water displacement , can be used to measure volume. Goal: Use water displacement to measure the volume of an object.

1. Get the Gizmo ready: Place the overflow cup under the faucet. Fill it until water starts to flow out of the spout. Place the 250 - mL beaker next to the overflow cup so that the spout of the overflow cup is over the beaker. (If necessary, empty the beaker into the sink.)
2. Measure: Place the sphere into the overflow cup, causing water to pour into the beaker. Empty the beaker into the 50 - mL graduated cylinder. Place the magnifier over the waterline. A. What is the volume of water in the graduated cylinder? 26 mL B. Recall that you used the ruler and the volume of a sphere equation to find the volume of the sphere in activity B. What is the volume of the sphere? 29. (Recall that 1 cm^3 is the same volume as 1 mL.)
3. Explain: Why does the water volume in the graduated cylinder match the sphere’s volume? The water volume matches with the sphere’s volume because they’re both volumes. Volume is the amount of space something takes up, so when putting the sphere in, to have it fit in, ~26 mL of water would need to come out.
4. Practice: Using what you have learned, find the volume of the rock. (Hint: For a more precise measurement, use the 25 - mL graduated cylinder .) What is the volume of the rock? About 8 mL Describe how you found the rock’s volume: I found the rock’s volume by measuring the amount of water that comes out from the overflow cup when the rock was put in. (Activity C continued on next page)

Activity C (continued from previous page)

5. Explore: You can find the volume of an object using just a graduated cylinder if you don’t have access to an overflow cup. This technique works if the object you are measuring is small enough to fit into the graduated cylinder. Return the overflow cup and the 25 - mL graduated cylinder to the cabinet. Take out the 100 - mL graduated cylinder and the pipette. Fill the 100 - mL graduated cylinder to exactly 40.0 mL, using the beaker and the pipette. A. Drag the rock into the 100 - mL graduated cylinder. Use the magnifier to read the new volume. What is the current water volume in the graduated cylinder? 48 mL B. How much has the water volume changed in the graduated cylinder? It’s changed by 8 mL C. Based on your answers to A and B, what is the volume of the rock? 8 mL
6. Practice: Use the same method to find the volume of the marble. Use the 25 - mL graduated cylinder. What is the volume of the marble? 1.2 mL Describe what you did to find the volume of the marble: I put 10 mL in the 25 - mL graduated cylinder and then dropped the marble inside. I saw the water rise to 11.2 mL, so I subtracted 10 mL from that and got 1.2 mL.
7. Think and discuss: When measuring the volume of the marble, why is it better to use the 25 - mL graduated cylinder than the 100 - mL graduated cylinder? If possible, discuss your answer with your classmates and teacher. It’s better to use the 25 - mL graduated cylinder rather than the 100 - mL one because a marble’s volume is small, so if we use a 100 - mL, it will be hard to detect any change at all in the water level once the marble is dropped in.
8. Further practice: Select Practice. Do the next four problems, using displacement to find the volume of the marble, rock, sphere, and rectangular prism. (Note: The dimensions of each object vary slightly each time you go through the problems.) Continue to practice as long as you like!