A floor limit is \(50~\text{lb}/\text{ft}^{2}\), and \(800~\text{lb}\) is uniformly spread over \(20~\text{ft}^{2}\). Calculate the load per square foot, make the safety comparison, and find \(\text{both}\) the per-square-foot margin and total remaining capacity.

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800/20=40 lb/ft²≤50; margin 10 lb/ft², total capacity 900 lb, remaining capacity 100 lb.

800/20=40 lb/ft²≤50; margin 10 lb/ft², total capacity 1,000 lb, remaining capacity 200 lb.

20/800=0.025 lb/ft²≤50; the load is within the limit with 799.5 lb remaining.

800/20=40, rounded to 50 lb/ft²; the load is at the limit with no margin.

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Curriculum context

Course: Math III
Standard: G-MG.2
Category: Geometry
Domain: Modeling with Geometry
Objective: Apply density concepts based on area and volume in modeling situations.
Problem type: Apply a per-unit rate to a typed resource or load decision