Unit 5 - Lesson 21 - Grade 8: Illustrative Mathematics
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Grade 8 Unit 5
Lesson 21: Cylinders, Cones, and Spheres
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 5
Lesson 21: Cylinders, Cones, and Spheres
CC BY 2021 Illustrative Mathematics®
Lesson: Cylinders, Cones, and Spheres
Sphere Arguments (Warm Up)
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.
1
1.
Do you agree with any of them? Explain your reasoning.
Sphere’s Radius (Optional)
1
2.
The volume of this sphere with radius r is V = 288π. This statement is true:
What is the value of r for this sphere? Explain how you know.
Info Gap: Unknown Dimensions
Round 1
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 be able to answer the question.
2. Ask your partner for the specific information that you need.
3. Explain how you are using the information to solve the problem.
Continue to ask questions until you have enough information to solve the problem.
If your teacher gives you the data card:
1. Silently read your card.
2. Ask your partner “What specific information do you need?” and wait for them to ask for information.
If your partner asks for information that is not on the card, do not do the calculations for them. Tell them you don’t have that information.
3. Before sharing the information, ask “Why do you need that information?” Listen to your partner’s reasoning and ask clarifying questions.
1
3.
Share the problem card and solve the problem independently.
Read the data card and discuss your reasoning.
Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.
Info Gap: Unknown Dimensions
Round 2
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 be able to answer the question.
2. Ask your partner for the specific information that you need.
3. Explain how you are using the information to solve the problem.
Continue to ask questions until you have enough information to solve the problem.
If your teacher gives you the data card:
1. Silently read your card.
2. Ask your partner “What specific information do you need?” and wait for them to ask for information.
If your partner asks for information that is not on the card, do not do the calculations for them. Tell them you don’t have that information.
3. Before sharing the information, ask “Why do you need that information?” Listen to your partner’s reasoning and ask clarifying questions.
1
4.
Share the problem card and solve the problem independently.
Read the data card and discuss your reasoning.
The Right Fit
1
5.
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.
Cone with a height of 8 centimeters and a radius of 3 centimeters.
Cylinder with a diameter of 6 centimeters and height of 2 centimeters.
Rectangular prism with a length of 3 centimeters, width of 4 centimeters, and height of 8 centimeters.
Sphere with a radius of 2 centimeters.
Cool Down: New Four Spheres
New Four Spheres
1
6.
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.
