Problem preview

G-GMD.5 Warmup M2-039-A07-V02

Apply scale factors to length, area, and volume using k, k^2, and k^3 relationships.

Apply a dilation factor to 1D, 2D, and 3D measures

Problem

For a dilation with \(k=1/2\), give separate multipliers for corresponding \(\text{one}\text{-}\text{dimensional}\) lengths/perimeters, \(\text{two}\text{-}\text{dimensional}\) areas/surface areas, and \(\text{three}\text{-}\text{dimensional}\) volumes.

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Length: 2; perimeter: 2; area or surface area: 4; volume: 8.

Length: one-half; perimeter: one-fourth; area or surface area: one-fourth; volume: one-eighth.

Length: one-half; perimeter: one-half; area or surface area: one-half; volume: one-half.

Length: one-half; perimeter: one-half; area or surface area: one-fourth; volume: one-eighth.

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Curriculum context

Course: Math II
Standard: G-GMD.5
Category: Geometry
Domain: Geometric Measurement and Dimension
Objective: Apply scale factors to length, area, and volume using k, k^2, and k^3 relationships.
Problem type: Apply a dilation factor to 1D, 2D, and 3D measures