Lesson 14

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volume of right prisms

Warm Up

Lesson

Summary

Cool

Down

Reflections

Student

Task

Learning

Targets

Practice Problems

Lesson Video

Unit 6

Functions and Volume

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14.1 Warm Up: three prisms with the same volume

Rectangles A, B, and C represent bases of three prisms.

1. If each prism has the same height, which one will have the greatest volume, and which will have the least. Explain your reasoning.

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• If each prism has the same volume, which one will have the tallest height, and which will have the shortest. Explain your reasoning.

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Learning Targets

• I can explain why the volume of a prism can be found by multiplying the area of the base and the height of the prism.

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14.2 Finding volume with cubes

BLACKLINE

MASTER (linked)

Your teacher will give you you snap cubes and the activity sheet. Use the applet if needed.

APPLET

1. Using the face of a snap cube as your area unit, what is the area of the shape? Explain or show your reasoning.

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• Use snap cubes to build the shape from the paper. Add another layer of cubes on top of the shape you have built. Describe this three-dimensional object.

3. What is the volume of your object? Explain your reasoning.

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• Right now, your object has a height of 2. What would the volume be
1. if it had a height of 5?
2. if it had a height of 8.5?

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14.3 can you find the volume?

APPLET

BLACKLINE

MASTER (linked)

1. Determine whether the shape is a prism.
2. For each prism, additionally:
1. Find the area of the base of the prism.
2. Find the height of the prism.
3. Calculate the volume of the prism.

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14.3 can you find the volume?

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14.3 Are you ready for more?

Imagine a large, solid cube made out of 64 white snap cubes. Someone spray paints all 6 faces of the large cube blue. After the paint dries, they disassemble the large cube into a pile of 64 snap cubes.

1. How many of those 64 snap cubes have exactly 2 faces that are blue?
2. What are the other possible numbers of blue faces the cubes can have? How many of each are there?
3. Try this problem again with some larger-sized cubes that use more than 64 snap cubes to build. What patterns do you notice?

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14.4 What’s the prisms height?

There are 4 different prisms that all have the same volume. Here is what the base of each prism looks like.

1. Order the prisms from shortest to tallest. Explain your reasoning.
2. If the volume of each prism is 60 units³, what would be the height of each prism?
3. For a volume other than 60 units³, what could be the height of each prism?
4. Discuss your thinking with your partner. If you disagree, work to reach an agreement.

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Lesson Summary

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Lesson Summary

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14.5 Cool Down: Octagonal Box

A box is shaped like an octagonal prism. Here is what the base of the prism looks like.

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For each question, make sure to include the unit with your answer and explain or show your reasoning.

1. If the height of the box is 7 inches, what is the volume of the box?

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• If the volume of the box is 123 in³, what is the height of the box?

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Reflections

• Can you explain why the volume of a prism can be found by multiplying the area of the base and the height of the prism?

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Practice Problems

Must Do: All Problems

Can Do: All Problems

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Lesson Video

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