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IM 8.5.21 Lesson: Cylinders, Cones, and Spheres

Author:GeoGebra Classroom Activities, IM 6 – 8 Math

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 cubic centimeters.
  • Tyler calculated 972 cubic centimeters.
  • Mai says it is cubic centimeters.
Do you agree with any of them?

Explain your reasoning.

The volume of this sphere with radius r is V = 288π.

This statement is true:  What is the value of for this sphere? Explain how you know.

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:If your teacher gives you the data 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.
  4. Share the problem card and solve the problem independently.
  5. Read the data card and discuss your reasoning.
  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.
  4. Read the problem card and solve the problem independently.
  5. Share 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. Use this space to take notes during the activity.

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.

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

For each of the figures from above, explain your reasoning.

A thirsty crow wants to raise the level of water in a cylindrical container so that it can reach the water with its beak.

  • The container has diameter of 2 inches and a height of 9 inches.
  • The water level is currently at 6 inches.
  • The crow can reach the water if it is 1 inch from the top of the container.
In order to raise the water level, the crow puts spherical pebbles in the container. If the pebbles are approximately inch in diameter, what is the fewest number of pebbles the crow needs to drop into the container in order to reach the water?

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