Minds On

Investigating volume

12 linking cubes were used to create a rectangular prism. How many ways can the cubes be arranged to make a prism? Use concrete or digital manipulatives, or any other method of your choice to explore.

A rectangular prism with a base of 2 cubes by 2 cubes and a height of 3 cubes. The top face is a square of 4 cubes.

Brainstorm

Brainstorm

What is the volume of your prism?

Calculate the area of the base and multiply it by the height of your prism.

Explore the volume of different prisms by clicking on Volume under each object.

Action

Calculating volume of prisms

To find the volume of a rectangular prism with a base of 2 cubes by 2 cubes and a height of 3 cubes, you would calculate the area of the base and then multiply it by the height of the object.

A rectangular prism with a base of 2 cubes by 2 cubes and a height of 3 cubes. The top face is a square of 4 cubes.

Press on the name of each 2-dimensional shape to review the area formula for them.

A = 1 2 b × h

A = l × w

A = π r 2

A = a + b 2 h

Calculate the volume of the prisms in the following organizer.

Complete the Volume of Prisms document in your notebook or using the following fillable and printable document.

Press the Activity button to access Volume of Prisms.

Activity (Open PDF in a new tab)

Design challenge

You and your team have been asked to design new packaging for a store. All packaging must have an identical height of 45 cm and should be a prism or cylinder.

Design two prisms and a cylinder as prototypes.

  • Ensure all of the heights are identical.
  • Record your thoughts. You may choose to do it as a sketch.
  • Estimate which one you believe will have the smallest volume.
  • Calculate the volume of each package.
  • Show your work.
  • Which package option do you recommend to the manufacturer?

Click on each name of a shape for the volume formulas you might use.

V = 1 2 b × h × height   of   prism

V = l × w × height   of   prism

V = π r 2 × height   of   prism

V = ( a + b ) 2 × h × height   of   prism

Student Success

Student success

Reflect and record your thoughts:

  • If possible, share your designs with someone else. What do you notice about the volumes?
  • Is there a relationship between the shape and size of the base and the volume?
  • Which prism did you estimate to have the smallest volume? Which prism had the smallest volume based on your calculations? How does your estimation compare?

Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.

Consolidation

Working with volume of prisms

A local candle company creates candles.

Calculate the volume of wax in each of the following candles. Record your results.

A cylinder that is 15 cm tall (height of prism).

  • Circular face has a diameter of 8 cm.

A triangular prism that is 8 cm tall (height of prism).

  • Triangular face has a base of 10 cm and a height of 10 cm.

A rectangular prism that is 20 cm tall (height of prism).

  • Rectangular face is 8 cm long and 12 cm wide.

Volume = Area of the base × height of the prism

There are samples of candles, in different prismatic shapes, on a tray.

Reflection

As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.

I feel...

Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.

When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.

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