Back to Apply density in area and volume — Problem 5 · Task Set 42

Exercises: Apply Concepts of Density Based on Area and Volume

Show your work for each problem. Every density answer must include its units. When a
problem asks you to type a number, read the stem carefully for the unit and the rounding
it expects.

Grade 10·24 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-mg-a-2

Work through problems with immediate feedback

Fluency Practice

A county reports a population density of $640$ people per square mile. Using $1 \text{ mi}^2 = 2.59 \text{ km}^2$ , what is this density in people per square kilometer?

About $1{,}658$ people per square kilometer, because the square-mile figure is scaled up by $2.59$ to reach the metric figure.

About $247$ people per square kilometer, because the same people are spread over $2.59$ times as many square kilometers as square miles.

About $398$ people per square kilometer, because $1$ mile is $1.609$ km and that factor converts the area in the denominator.

$640$ people per square kilometer, because the county still contains exactly the same residents after the conversion, so the density figure describing them stays at $640$ as well.