Measuring Volume Part B

Name: Date: Student Exploration: Measuring Volume Part B Vocabulary: cubic centimeter, diameter, graduated cylinder, meniscus, milliliter, pipette, radius, rectangular prism, sphere, volume, water displacement Activity B: Select the Free Exploration mode.. Regular solids 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 (cm³). 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? 8cm. B. How does the area of the rectangle relate to the lengths of each side? The more you add to each side the greater the area will be. 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 cm³, or 1 mL.. A. What are the length, width, and height of the block? Length: 3cm Width: 3cm Height: 4cm B. Multiply these three dimensions. What is the product of the length, width, and height? 36cm^3 C. How many cubic centimeters are in the block? 36cm^3 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. (Activity B continued on next page) A. What are the length, width, and height of the block? Length: 4.2cm Width: 2.7cm Height: 7.6cm B. What is the volume of the block? 86.18cm^3 4. Measure: Return the block to the cabinet and drag out the large sphere. The volume of a sphere is calculated using the following formula: V=4m³/3 The symbol in represents the number pi, which is about 3.14. The letter rstands for the radius of the sphere, which is the distance from the center of a sphere to its surface. The radius is exactly half of the diameter, which is the distance across the sphere. (The diameter is also equal to the length, width, and height of the sphere.) A. Place the ruler over the sphere. What is the diameter of the sphere? 3.7cm B. What is the radius of the sphere? 1.85cm C. What is the volume of the sphere? 26.52cm^3 5. Measure: Return the large sphere to the cabinet and drag out the small marble. Use the ruler and your calculator to find the volume of the marble. Show your work. V=4(3.14)^3 (1.3) = 9.2cm^3 3 Volume of the marble: 9.2cm^3 6. Further practice: Select Practice. Do the next three problems, measuring the sphere, the marble, and the rectangular prism. (Note: The dimensions of each object vary slightly each time you go through the problems.) Sphere-V = 57.91cm^3 Marble-V7.24cm^3 Rectangular prism-V 39.64cm^3 Get the Gizmo ready: Activity C: Select Free Exploration. Water displacement 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 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? 26.8mL 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? 26.52 (Recall that 1 cm³ is the same volume as 1 mL.) 3. Explain: Why does the water volume in the graduated cylinder match the sphere's volume? It matches because when the sphere was dropped into the water it poured out the volume of the sphere. 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? 7.2mL Describe how you found the rock's volume: I dropped it into the overflow cup and let the water that overflowed go into the 250 ml. beaker, Then I poured what's in the 250 ml. beaker into the 25 mL graduated cylinder and measured how much there was in it. (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? 47.9mL B. How much has the water volume changed in the graduated cylinder? It changed by 7.9 mL C. Based on your answers to A and B, what is the volume of the rock? 7.9cm 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? 2cm Describe what you did to find the volume of the marble: I filled the 25mL cylinder to 20mL then put the marble inside it. Then, I measured the volume and subtracted the new volume by the old volume and found the difference. 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. Its better because you can more accurately find the volume. 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! Marble-V1mL Rock-V=9mL Sphere-V22.7mL Rectangular prism-V = 98mL