Lesson 25

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cylinders, cones, and spheres

Warm Up

Lesson

Summary

Cool

Down

Reflections

Student

Task

Learning

Targets

Practice Problems

Lesson Video

Unit 6

functions and volume

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25.1 Warm Up - Sphere Arguments

Four students each calculated the volume of a sphere with a radius of 9 centimeters and they got four different answers.

• Han thinks it is 108 cubic centimeters.
• Jada got 108𝜋 cubic centimeters.
• Tyler calculated 972 cubic centimeters.
• Mai says it is 972𝜋 cubic centimeters.

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Do you agree with any of them? Explain your reasoning.

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Learning Targets

• I can find the radius of a sphere if I know its volume.
• I can solve mathematical and real-world problems about the volume of cylinders, cones, and spheres.

Success Criteria

Today I am using the volume of a sphere to see what happens to the volume when I change a value of a dimension.

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25.2 Sphere’s Radius

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25.3 Info Gap: Unknown Dimensions

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the problem card:

1. Silently read your card and think about what information you need to answer the question.
2. Ask your partner for the specific information that you need.
3. Explain to your partner how you are using the information to solve the problem.
4. Solve the problem and explain your reasoning to your partner.

If your teacher gives you the data card:

1. Silently read the information on your card.
2. Ask your partner “What specific information do you need?” and wait for your partner to ask for information. Only give information that is on your card. (Do not figure out anything for your partner!)
3. Before telling your partner the information, ask “Why do you need that information?”
4. After your partner solves the problem, ask them to explain their reasoning and listen to their explanation.

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25.4 The Right Fit

A cylinder with diameter 3 centimeters and height 8 centimeters is filled with water. Decide which figures described here, if any, could hold all of the water from the cylinder. Explain your reasoning.

1. Cone with a height of 8 centimeters and a radius of 3 centimeters.
2. Cylinder with a diameter of 6 centimeters and height of 2 centimeters.
3. Rectangular prism with a length of 3 centimeters, width of 4 centimeters, and height of 8 centimeters.
4. Sphere with a radius of 2 centimeters.

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Lesson Summary

• Describe some relationships between the volumes of cylinders, cones, and spheres.
• How do we find a missing dimension when we know the volume and another dimension of a cylinder, cone, or sphere (or just the volume in the case of the sphere)?
• What happens to the volume of a cylinder or cone when its height is doubled? Tripled?
• What happens to the volume of a sphere when its height is doubled? Tripled?
• What happens to the volume of a cylinder, cone, or sphere when its radius is doubled? Tripled?
• What happens to the volume of a cylinder or cone when its height is doubled and its radius is halved?
• What happens to the volume of a cylinder or cone when its radius is doubled and its height is halved?

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Some information is given about each sphere. Order them from least volume to greatest volume. You may sketch a sphere to help you visualize if you prefer.

Sphere A: Has a radius of 4

Sphere B: Has a diameter of 6

Sphere C: Has a volume of 64𝜋

Sphere D: Has a radius double that of sphere B.

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25.5 Cool Down: New Four Spheres

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Reflections

• Can you find the radius of a sphere if I know its volume?
• Can you solve mathematical and real-world problems about the volume of cylinders, cones, and spheres?

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Practice Problems

Must do: All problems

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Lesson Video

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