A rooftop deck limit is \(45~\text{lb}/\text{ft}^{2}\), and a \(1,000\text{-}\text{lb}\) setup 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 overload and total excess load.

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1,000/20=50 lb/ft²>45; overload 5 lb/ft², total capacity 1,000 lb, excess load 0 lb.

1,000/20=50 lb/ft²>45; overload 5 lb/ft², total capacity 900 lb, excess load 100 lb.

20/1,000=0.02 lb/ft²≤45; the setup is within the limit.

1,000/20=50, rounded down to 45 lb/ft²; the setup is at the limit.

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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