School-entry solid geometry develops section and rotation reasoning, justified polygon and slab limits, Cavalieri comparisons, contextual volume calculations and density-based design. Exact computations and written arguments supply reviewable evidence; this unit does not claim complete geometry mastery.
Open any lesson. Completion records participation; automatic practice checks and human judgment of written arguments are separate. This unit retains its own versioned requirements.
Readiness and preparation
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Try these short questions on paper, then compare your reasoning. They are optional self-checks, not a placement score or a navigation requirement. Use a targeted review when useful and return with your browser’s Back control.
How do length, area and volume change under a scale factor k?
Sections and similar cones use different powers of a length scale.
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For k>0, lengths multiply by k, areas by k² and volumes by k³. A cross-section area needs square units; multiplying it by a perpendicular thickness gives cubic units.
A sloping edge is not the height used in a volume formula.
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Height is the distance between parallel base planes, measured perpendicular to them. A right triangle can relate it to a sloping length when the corresponding right angle is justified.
Composite solids and removed material need a valid decomposition.
Compare reasoning and find a refresher
Add non-overlapping pieces (shared boundaries do not contribute area). Subtract a hole only if it is actually contained in the original region. Track the same units throughout.
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