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VOLUMES OF CONES, CYLINDERS, AND SPHERES STORYBOARDS

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Your parents have decided to buy a pool for your backyard. How exciting! The only problem is that they can’t decide if they should put in an above- ground circular pool or an in-ground rectangular pool. Here are the dimensions for each option: Above-ground circular pool: 6 feet deep with a radius of 12 feet In-ground rectangular pool: 40 feet long, 16 feet wide, and 4 feet deep. Since you are learning about volume in your math class at school, they ask you to help them decide. You, of course, think they should go with the bigger pool. So, which pool is bigger (holds more water)? INTRODUCTION Imagine this scenario: (Read onscreen content). How could you help your parents decide which pool to buy? (Wait until student responds with “Find the volume of each pool.”) So, how would we find the volume of the above-ground circular pool? What type of figure is this pool? (Wait for student response of “Cylinder”.) Do we know how to find the volume of a cylinder? (Student(s) will most likely respond with “no”.) What about the other pool? What type of figure is this? (Wait for student response of “Rectangular prism”.) Can we find the volume of this pool? (Student(s) will most likely respond with “yes”.) So, now we need to learn how to find the volume of a cylinder, which is exactly where our lesson begins! Click on the “next” button to navigate to Slide #2. Slide #1 Onscreen Content Detailed Script Interactivity / Navigation 4 ft 40 ft 16 ft 12 ft 6 ft

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Prior Knowledge: Concept of “area” How to find the area of a circle Concept of “volume” How to find the volume of a prism How to find the volume of a pyramid Knowledge of exponents, such as “squared” and “cubed” PRIOR KNOWLEDGE In previous lessons, you have learned about area and volume. You learned what the concepts of “area” and “volume” mean. You have learned how to find the areas of many two-dimensional figures, including circles. You have learned how to find the volumes of some three-dimensional solids, such as prisms and pyramids, through discovery of their formulas. During this lesson, you will discover, memorize, and use the formulas for finding the volumes of cylinders, cones, and spheres. The instructor will be able to click on the image of a circle and the formula for the area of a circle will appear. The instructor will be able to click on the image of a prism and the formula for the volume of a prism will appear. The instructor will be able to click on the image of a pyramid and the formula for the volume of a pyramid will appear. Slide #2 Onscreen Content Detailed Script Interactivity / Navigation

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1)Students will be able to memorize the formulas for the volume of a cylinder, cone, and sphere. 2)Students will be able to explain how the formulas for the volume of a cylinder, cone, and sphere were derived. 3)Students will be able to use and apply the formulas for the volume of a cylinder, cone, and sphere to solve real-world problems. OBJECTIVES Here are your objectives for this lesson: First, you will be able to memorize the formulas for finding the volumes of cylinders, cones, and spheres. Next, you will be able to explain how these formulas were derived. Lastly, you will be able to use and apply these formulas to solve real-world problems. The objectives will appear one-by-one as the screen is clicked so that student focus is on one objective at a time. Slide #3 Onscreen Content Detailed Script Interactivity / Navigation

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THE VOLUME OF A CYLINDER When the instructor clicks on the question “Where did the formula for the volume of a cylinder come from?” a website will open with a video showing how the formula is derived. The video is approximately 5 minutes long. Slide #4 Onscreen Content Detailed Script Interactivity / Navigation Where did the formula for the volume of a cylinder come from?

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THE VOLUME OF A CONE When the instructor clicks on the question “Where did the formula for the volume of a cone come from?” a website will open with a video showing how the formula is derived. The video is approximately 4 ½ minutes long. Slide #5 Onscreen Content Detailed Script Interactivity / Navigation Where did the formula for the volume of a cone come from?

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THE VOLUME OF A SPHERE When the instructor clicks on the question “Where did the formula for the volume of a sphere come from?” a website will open with a video showing how the formula is derived. The video is approximately 5 minutes long. Slide #6 Onscreen Content Detailed Script Interactivity / Navigation Where did the formula for the volume of a sphere come from?

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1)How can we find the volume of a cylinder that has a radius of 8 feet and a height of 10 feet? 2)How can we find the volume of a cone that has a radius of 5 inches and a height of 7 inches? 3)How can we find the volume of a sphere that has a radius of 6 meters? GUIDED PRACTICE There will be a labeled figure/graphic to go along with each problem. Let’s solve these problems together. Before we begin, I will distribute a handout that contains all of the formulas we have just learned. Please use this handout whenever you need to for the duration of this lesson. Each problem will appear one-by-one when the slide is clicked so that students are focused on only one problem at a time. The graphics will also only appear when the problem appears. Slide #7 Onscreen Content Detailed Script Interactivity / Navigation

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Practice: Find the volume of the following 3-D solids. Round to the nearest hundredth. 1)Cylinder with a radius of 3 feet and a height of 7 feet. 2)Cylinder with a radius of 8 meters and a height of 5 meters. 3)Cone with a radius of 6 inches and a height of 4 inches. 4)Cone with a radius of 10 millimeters and a height of 12 millimeters. 5)Sphere with a radius of 5 centimeters. 6)Sphere with a diameter of 8 kilometers. INDEPENDENT PRACTICE There will be labeled figures/graphics to go along with each problem. Now we will practice with each of the formulas given some information about a cylinder, cone, or sphere. Make sure all work is shown on your paper, including the original formula. These problems can be worked on with a partner. I will walk around to check your work and solutions. Please stop me if you have any questions as you are working. (When students have finished working…) We will now go over each problem. (Click on each problem to reveal the steps to solve and the answer.) Slide #8 Onscreen Content Detailed Script Interactivity / Navigation

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Your parents have decided to buy a pool for your backyard. How exciting! The only problem is that they can’t decide if they should put in an above- ground circular pool or an in-ground rectangular pool. Here are the dimensions for each option: Above-ground circular pool: 6 feet deep with a radius of 12 feet In-ground rectangular pool: 40 feet long, 16 feet wide, and 4 feet deep. Since you are learning about volume in your math class at school, they ask you to help them decide. Can you help them figure out the volume of each pool? REAL-WORLD PROBLEMS Slide #9 Onscreen Content Detailed Script Interactivity / Navigation 12 ft 6 ft 4 ft 40 ft 16 ft

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A cylindrical tank has a height of 10 feet and a radius of 4 feet. Jane fills the tank with water at a rate of 8 cubic feet per minute. At this rate, how many minutes will it take Jane to completely fill the tank without overflowing it? Round your answer to the nearest minute. REAL-WORLD PROBLEMS There will be a labeled figure/graphic to go along with this problem. Here is another real-life scenario. Take a moment to read the problem to yourself. (Pause for students to read.) Would someone like to read this problem out loud? (Choose student volunteer to read problem out loud.) Thank you. Now, what are they asking us to find? (Pause for student responses.) What information do they give us? (Pause for student responses.) What is the process we must use in order to solve this problem? (Pause for student responses.) With your partner, I would like you to use what we’ve learned and try to solve this problem. As you are working, I will walk around to check your work and solutions. Please stop me if you have any questions. (When students have finished working…) Would anyone like to share how they solved this problem? (Allow students to explain the process and solution to the problem, while guiding them towards the correct process and answer.) Slide #10 Onscreen Content Detailed Script Interactivity / Navigation

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1) The dimensions of three wooden models are given below. Which has the greatest volume? A.A cylinder with diameter 8 inches and height 6 inches B.A cone with radius 8 inches and height 6 inches C.A sphere with diameter 8 inches 2) This cone and sphere have equal volumes. What is the radius of the sphere? 3) Show and/or explain how the formulas for the volume of a cone, cylinder, and sphere were derived. FORMATIVE EVALUATION 1)There will be labeled figures/graphics to go along with this problem. 2)See graphics below. 3)No graphics are needed. Take a moment to read these problem to yourself. (Pause for students to read.) Would someone like to read these problems out loud? (Choose student volunteer to read problems out loud.) Thank you. I would now like you to solve each one of these problems independently. As you are working, I will walk around to check your progress and understanding. Please stop me if you have any questions. (When students have finished working…) I will not be collecting your work to evaluate your individual understanding of the lesson. Click on the “next” button to navigate to Slide #12. Slide #11 Onscreen Content Detailed Script Interactivity / Navigation

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Your final assessment for this lesson will be completed on the computer. SUMMATIVE ASSESSMENT Your final assessment for this lesson will be completed on the computer. You also have the option of taking the assessment on paper. You will be allowed to use calculators for this assessment. You must work independently on this assessment. Click on the “next” button to navigate to Slide #13. Slide #12 Onscreen Content Detailed Script Interactivity / Navigation

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Congratulations on your completion of this lesson on finding the volume of cylinders, cones, and spheres! CONGRATULATIONS! Congratulations on your completion of this lesson! In this lesson, you have learned the formulas for finding the volume of cylinders, cones, and spheres. You have learned where the formulas came from and were required to explain where they came from on your final assessment. You were also required to use and apply these formulas to solve real-world problems. No further navigation is required. Slide #13 Onscreen Content Detailed Script Interactivity / Navigation

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