Grade 10 · Distinguish length and cubic scale · 35 of 750
Distinguish length and cubic scale · practice 4
A rectangular prism has length 2.5, width 4.5, and height 4.5. 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 2.5, width 4.5, and height 4.5. 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.
A starting point
First find the area of one horizontal layer.
Work through the reasoning
Step 1
Translate the givens
One layer has area 2.5 × 4.5 = 11.25 square units.
Step 2
Calculate with the model
Stack through height 4.5: V = 11.25 × 4.5 = 50.625 cubic units.
Step 3
Check and interpret
Divide volume by base area: 50.625 ÷ 11.25 = 4.5, recovering height. Three length factors produce cubic units.
The answer
50.625 cubic units.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
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
PausedHD animation studio
From experiment to screen.
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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 = 2.5; Width = 4.5; Height = 4.5.
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.