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G-MG.3 Warmup M3-041-A04-V02

Use geometric methods to solve design problems under constraints such as cost, space, or ratios.

Separate length, area, and volume scale factors

Problem

A model's corresponding lengths are scaled from the real object by \(k~=~1/20\). State the model-to-real length, area, and volume factors and classify the scaling as an enlargement or reduction.

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Model lengths, areas, and volumes are each 1/20 of the real object because every measurement is treated as linear.

Model lengths are 1/20 of real lengths, model areas are 1/400, and model volumes are 1/8000. This is a reduction from the real object to the model.

Model lengths, areas, and volumes are 20, 400, and 8000 times the real object, reversing the stated direction.

Model lengths are 1/20, areas are 1/8000, and volumes are 1/400, which swaps the squared and cubed factors.

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Curriculum context

Course: Math III
Standard: G-MG.3
Category: Geometry
Domain: Modeling with Geometry
Objective: Use geometric methods to solve design problems under constraints such as cost, space, or ratios.
Problem type: Separate length, area, and volume scale factors