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All courses Math Foundations · MF.GM.7 54 of 60
Set up and solve contextual measurement problems that require choosing the correct geometric formula and units.

Identify what the context is asking to measure

Problem
Mia wants to paint the outside of a rectangular storage box. Name the geometric quantity that measures how much surface must be covered.
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Hint

Focus on the words "paint the outside" of the rectangular box. Ask yourself: is Mia measuring around an edge, one flat face, all outer faces, or the space inside?

For 3D objects, covering the outside means adding up the exposed faces. That is different from perimeter (around), area of one flat region, or volume (inside space).

Solution walkthrough

01

Identify what paint covers

\[\text{paint}~\text{covers}~\text{the}~\text{outside}~\text{faces}~\text{of}~\text{the}~\text{box}\]

The task concerns the two-dimensional exterior surfaces, not the space inside or the edge lengths.

02

Match the request to a measure

\[\text{total}~\text{area}~\text{of}~\text{all}~\text{exterior}~\text{faces}=\text{surface}~\text{area}\]

Surface area combines the areas of every outside face of a three-dimensional object.

03

Distinguish volume

\[\text{volume}~\text{measures}~\text{interior}~\text{capacity}~≠~\text{painted}~\text{covering}\]

Volume would answer how much the box holds, not how much paint covers it.

04

Distinguish perimeter

\[\text{perimeter}~\text{measures}~a~\text{two}-\text{dimensional}~\text{boundary}~≠~\text{all}~\text{prism}~\text{faces}\]

A single boundary length does not count the areas of the box's faces.

05

Name the quantity

\[\text{Surface}~\text{area}\]

The geometric quantity for the total outside covering is surface area.

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Another way

  1. Imagine unfolding the box into a net and adding the areas of all rectangles; that sum is surface area.

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Common mistake

Do not choose volume; painting the outside uses square units, while volume uses cubic units.