Problem preview
G-GMD.5 Warmup M2-039-A11-V01

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

Interpret dimensional measure multipliers in context

Problem

A cube's side length doubles. How do its surface area and volume change?

Big Picture

What this problem is really about

Doubling an edge does not make every measure merely double, because surface area and volume combine different numbers of length directions. We’ll translate the edge change into a linear factor, square it for the two-dimensional faces, cube it for the three-dimensional interior, and connect those powers to the cube’s measures.

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Four variants of this problem type
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
Interpret dimensional measure multipliers in context