Apply density concepts based on area and volume in modeling situations.
Find the total quantity when density and area are given
Problem
If the density is \(400~\text{people}~\text{per}~\text{square}~\text{mile}\) and the area is \(12~\text{square}~\text{miles}\), what is the total quantity?
Big Picture
What this problem is really about
A density is a unit rate, so recover a total by accumulating that rate across the entire area. Multiply quantity per square unit by the number of square units and track the units as factors. The area units cancel, leaving the total quantity alone; that cancellation is a reliable check that multiplication, rather than division, matches the question.
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