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Grade 5 · Volume

Solar-project planning: stack equal layers of unit cubes

A model box for a model solar-energy project is 1 unit cubes long, 2 wide, and 1 layers high. Change the controls and explain what the animation reveals.

Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.

Watch the relationship

Paused
Solar-project planning: stack equal layers of unit cubes. Cubes placed: 0. Cubes per layer: 2. Full volume in cubic units: 21 × 2 × 1 = 2 cubic unitsPlaced 0 cubes · 2 in each full layer
The box is a rectangular prism filled by congruent unit cubes. Perspective is a drawing convention; cubes hidden from view are still counted. Only whole edge lengths are used.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

Cubes placed
0
Cubes per layer
2
Full volume in cubic units
2

HD animation studio

From experiment to screen.

Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.

Understand what you are seeing

The idea behind the motion.

A model box for a model solar-energy project is 1 unit cubes long, 2 wide, and 1 layers high. Volume counts the unit cubes that fill a solid without gaps or overlaps. First count one rectangular layer, then multiply by the number of equal layers. Each layer contains 2 cubes, and 1 layers contain 2. Cubic units describe occupied space, not the outside surface area.

A relationship to keep

V = 1 × 2 × 1 = 2 cubic units

Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.

  1. STEP 1

    Read the starting situation

    A model box for a model solar-energy project is 1 unit cubes long, 2 wide, and 1 layers high. Identify what each number measures before changing a control; the worked example refers to these starting values.

  2. STEP 2

    Follow the mathematical change

    Place cubes one layer at a time. Some cubes become hidden behind others in the perspective drawing, but they still contribute to the volume. Pause on an intermediate frame and compare the picture with the live readouts.

  3. STEP 3

    Explain and test the relationship

    Each layer contains 2 cubes, and 1 layers contain 2. Cubic units describe occupied space, not the outside surface area. Change one input, predict its effect, and test whether the same relationship still works.

Your turn to explain

Make a prediction. Test your reasoning.

Solar-project planning: use the original situation. A model box for a model solar-energy project is 1 unit cubes long, 2 wide, and 1 layers high. How many cubes are needed for one additional full layer?

Use the values specified in the question. Reset restores the initial values for this investigation.

Compare your explanation

2 additional cubes. The new volume would be 4 cubic units.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 5 · Geometry

Derive the box-volume formula

Multiply length, width, and height for a rectangular prism.