Exercises: Apply Concepts of Density Based on Area and Volume

$480$ miles per gallon, because $480$ is the total distance the car covered on that tank of fuel, and that total is what the trip is measured by.

$40$ miles per gallon, because dividing $480$ miles by $12$ gallons gives the distance covered per single gallon.

$5{,}760$ miles per gallon, because multiplying $480$ miles by $12$ gallons combines the two given amounts.

$0.025$ gallons per mile is the only correct rate, because fuel must always be the numerator of a fuel rate.

$2.7$, since dividing $891$ by $330$ gives $2.7$ and that number is the density.

$2.7 \text{ cm}^3\text{/g}$, since density compares the volume the metal occupies to each gram of its mass.

$294{,}030 \text{ g} \cdot \text{cm}^3$, since the mass and the volume both describe the block and are combined to describe it.

$2.7 \text{ g/cm}^3$, since density is mass divided by volume and the units divide the same way.

$945$ g, because mass is density multiplied by volume, and $\text{g/cm}^3 \times \text{cm}^3$ leaves grams.

$352.7$ g, because the density and the volume are two amounts of the same material and can be added together.

$347.3$ g, because the density has to be removed from the volume to leave only the mass behind.

$129.6$ g, because density is mass over volume, so the volume is divided by the density to recover the mass.

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.