Math With AmarA C A D E M Y

Grade 10 · Distinguish length and cubic scale · 622 of 750

Distinguish length and cubic scale · practice 67

A rectangular prism has length 1, width 4, and height 6.5. Find its volume. Follow the calculation, then test the quantities in the animated example.

Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.

01 · Make a prediction

Your practice question

A rectangular prism has length 1, width 4, and height 6.5. Find its volume.

Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.

02 · Explore the model

See the mathematical relationship move.

Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.

Watch the relationship

Paused
Distinguish length and cubic scale · practice 67. Fill fraction: 0%. Filled volume: 0. Capacity: cubic units: 26Build a prism from equal base-area layersDimensions 1 × 4 × 6.5Filled volume: 0 of 26
The prism is an ideal box with negligible wall thickness. The drawing is an oblique projection, so apparent angles and edge lengths are not measurements. The numerical controls supply the actual dimensions.

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.

Fill fraction
0%
Filled volume
0
Capacity: cubic units
26

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.

The mathematical idea

A rectangular prism can be built from horizontal layers of equal base area. Multiplying length by width gives one layer's area; multiplying by height accumulates the entire volume. A change in all three lengths multiplies volume by the cube of the length scale. Starting quantities: Length = 1; Width = 4; Height = 6.5.

V = length × width × height

03 · Reflect and transfer

Explain what changes and why.

If every edge doubles, why does volume multiply by eight rather than two?

This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.