Volume Formula For Rectangular Prisms

Volume Formula For Rectangular Prisms

Volume of Cubes

Opening

Volume of Cubes

The cube at the left of the diagram has edge lengths of 1 unit. The cube at the right has edge lengths of 14 unit.

Volume is the amount of space inside a 3-D figure.

  • How many 14-unit cubes fit inside the 1-unit cube?
  • What is the volume of the 14-unit cube?

Math Mission

Opening

Build rectangular prisms with fractional edge lengths and find the volume of the prisms.

Find the Volume of Prisms

Work Time

Find the Volume of Prisms

When a rectangular prism has whole-number edge dimensions, you can find its volume using the formula V = l ⋅ w ⋅ h, where l, w, and h represent the length, width, and height of the prism. Investigate whether this formula works even if the dimensions are not whole numbers.

Use the 14-unit cubes to build a prism with a length of 114 units, a width of 34units, and a height of 12 unit.

  • How many 14-unit cubes fit inside the prism?
  • What is the volume of the prism?
  • Does the volume formula
    V = l ⋅ w ⋅ h (or V = lwh) work for this prism?

INTERACTIVE: Cube Builder

Hint:

How many 14 -unit cubes fit inside a 1-unit cube?

The Formula

Work Time

The Formula

Use the 13-unit cubes to build a prism with a length of 123 units, a width of 113 units, and a height of 23 unit.

  • How many 13-unit cubes fit inside the prism?
  • What is the volume of each 13-unit cube?
  • What is the volume of the prism?
  • Does the volume formula V = lwh work for this prism?

INTERACTIVE: Cube Builder

Hint:

How many 13-unit cubes fit inside a 1-unit cube?

Applying the Formula

Work Time

Applying the Formula

  • Use the volume formula to find the volume of a prism with a length of 45 unit, a width of 35 unit, and a height of 25 unit.

Using the Formula

Work Time

Using the Formula

  • Calculate the volume of each of the two prisms you made in Lesson 1.
  • Was your prediction about which prism has the greater volume correct?

Hint:

Use the formula to find the volume of the prisms.

Prepare a Presentation

Work Time

Prepare a Presentation

  • Explain how you found the volume of one of the cubes from the lesson.
  • Explain how you found the volume of one of the rectangular prisms from the lesson.
  • Support your explanations with diagrams.

Challenge Problem

This video shows an act in which a man does acrobatics inside of a cube.

  • Estimate the volume of the cube.
  • Estimate the percentage of the volume of the cube that is taken up by the man’s body.

VIDEO: Aerial Cube Act

Make Connections

Performance Task

Ways of Thinking: Make Connections

  • Take notes about your classmates’ methods for finding the volume of a cube and a rectangular prism.

Hint:

As your classmates present, ask questions such as:

  • What problems did you encounter in finding the volume?
  • What knowledge of multiplying fractions did you use?
  • Did you make an estimate of the volume first? How did you make your estimate?
  • How did the Cube Builder help you?
  • How do you know your answer is correct?

Volume of Rectangular Prisms

Formative Assessment

Summary of the Math: Volume of Rectangular Prisms

  • Write a summary about how to build and find the volume of rectangular prisms.

Hint:

Check your summary.

  • Do you explain how to build a prism with cubes and find the volume of the prism?
  • Do you provide a formula for finding the volume of any rectangular prism?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

I like using a formula to find volume because …