Relate area and volume under scaling
See this course’s project requirements
A geometry explanation board with angle deductions, congruence and similarity tests, a scale argument and a checked space-design decision.
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What to include
- Keep every given and correspondence visible.
- Show angle deductions with their reasons.
- Distinguish congruence from similarity.
- Check length, area and volume scale factors.
- Write a final panel explanation and all changed-case responses.
Review and revise
Use these criteria to check your work and choose what to improve.
- Method: applies the course-specific rules to the supplied cases with visible intermediate work.
- Accuracy: results agree with the stated facts, units, boundaries and independent checks.
- Reasoning: explains why the result follows and identifies a limitation or unresolved question.
- Transfer: completes changed cases and revises the final project when a relevant assumption changes.
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The idea in everyday life
Case: rectangle 2 cm×3 cm and box 2 cm×3 cm×4 cm are enlarged with length factor 2.
Scaling every length by k multiplies area by k² and volume by k³. This differs from adding k to dimensions. Separate linear, area and volume units.
Relate area and volume under scaling — worked practice
Scaling every length by k multiplies area by k² and volume by k³. This differs from adding k to dimensions. Separate linear, area and volume units.
Case: rectangle 2 cm×3 cm and box 2 cm×3 cm×4 cm are enlarged with length factor 2.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Case: rectangle 2 cm×3 cm and box 2 cm×3 cm×4 cm are enlarged with length factor 2. |
Copy as plain text
1. 1. Baseline
Calculate original area and volume.
You should see: Area 6cm²; volume 24cm³.
2. 2. Scale lengths
Double each dimension.
You should see: Rectangle 4×6; box 4×6×8 cm.
3. 3. Calculate
Find enlarged area and volume.
You should see: Area 24cm²; volume 192cm³.
4. 4. Compare factors
Divide enlarged by original.
You should see: Area factor 4; volume factor 8, not factor 2.
What to finish
A dimension, area and volume scaling comparison with units.
Watch for this
Length×width gains 2×2=4.
How can I tell I understand it?
Explain why doubling all lengths multiplies area by four and volume by eight.
Quick knowledge check
Answer all 3 questions. Get at least 2 right and the lesson completes automatically.
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Answer all 3 questions above and get at least 2 right. You can review the explanations and try again.
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Source & access notes · checked 2026-10-01
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