The cube at the left of the diagram has edge lengths of 1 unit. The cube at the right has edge lengths of $\frac{1}{4}$ unit.

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

How many $\frac{1}{4}$-unit cubes fit inside the 1-unit cube?

What is the volume of the $\frac{1}{4}$-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 $\frac{1}{4}$-unit cubes to build a prism with a length of 1$\frac{1}{4}$ units, a width of $\frac{3}{4}$units, and a height of $\frac{1}{2}$ unit.

How many $\frac{1}{4}$-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?

Use the $\frac{1}{3}$-unit cubes to build a prism with a length of 1$\frac{2}{3}$ units, a width of 1$\frac{1}{3}$ units, and a height of $\frac{2}{3}$ unit.

How many $\frac{1}{3}$-unit cubes fit inside the prism?

What is the volume of each $\frac{1}{3}$-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 $\frac{1}{3}$-unit cubes fit inside a 1-unit cube?

Use the volume formula to find the volume of a prism with a length of $\frac{4}{5}$ unit, a width of $\frac{3}{5}$ unit, and a height of $\frac{2}{5}$ 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.