Density from area and volume Practice Questions (Grade 9)

Warm-upeasy

Riverside has a population density of $1{,}250$ people per square mile and an area of $48$ square miles. What is the population of Riverside?

Set up the proportion $\dfrac{1{,}250\text{ people}}{1\text{ square mile}} = \dfrac{x\text{ people}}{48\text{ square miles}}\textsf{.}$ Cross-multiplying gives $x = 1{,}250 \times 48 = 60{,}000\text{ people}\textsf{.}$

Mid-gameeasy

A ranch has $414$ cattle and a density of $18$ cattle per acre. What is the area of the ranch, in acres?

Set up the proportion $\dfrac{18\text{ cattle}}{1\text{ acre}} = \dfrac{414\text{ cattle}}{x\text{ acres}}\textsf{.}$ Cross-multiplying gives $18x = 414\textsf{,}$ so $x = 23\text{ acres}\textsf{.}$

Mid-gameeasy

A city park has a density of $35$ picnic tables per acre and covers $24$ acres. How many picnic tables are in the park?

Set up the proportion $\dfrac{35\text{ picnic tables}}{1\text{ acre}} = \dfrac{x\text{ picnic tables}}{24\text{ acres}}\textsf{.}$ Cross-multiplying gives $x = 35 \times 24 = 840\text{ picnic tables}\textsf{.}$

Mid-gamemedium

A storage tank holds liquid at a density of $8$ pounds per cubic foot. If the tank contains $1{,}920$ pounds of liquid, what is the volume of the liquid, in cubic feet?

Set up the proportion $\dfrac{8\text{ pounds}}{1\text{ cubic foot}} = \dfrac{1{,}920\text{ pounds}}{x\text{ cubic feet}}\textsf{.}$ Cross-multiplying gives $8x = 1{,}920\textsf{,}$ so $x = 240\text{ ft}^{3}\textsf{.}$

Mid-gamemedium

A shipping crate has a volume of $160$ cubic feet and holds $4{,}800$ identical packages. What is the packaging density, in packages per cubic foot?

Set up the proportion $\dfrac{x\text{ packages}}{1\text{ cubic foot}} = \dfrac{4{,}800\text{ packages}}{160\text{ cubic feet}}\textsf{.}$ Cross-multiplying gives $160x = 4{,}800\textsf{,}$ so $x = 30\text{ packages per ft}^{3}\textsf{.}$

Mid-gamemedium

A room heater uses energy at a density of $25$ BTUs per cubic foot. For a room with volume $120$ cubic feet, how many BTUs does the heater use?

Set up the proportion $\dfrac{25\text{ BTUs}}{1\text{ cubic foot}} = \dfrac{x\text{ BTUs}}{120\text{ cubic feet}}\textsf{.}$ Cross-multiplying gives $x = 25 \times 120 = 3{,}000\text{ BTUs}\textsf{.}$

Mid-gamemedium

Lakeview has a population of $37{,}800$ people and an area of $84$ square miles. What is the population density, in people per square mile?

Set up the proportion $\dfrac{x\text{ people}}{1\text{ square mile}} = \dfrac{37{,}800\text{ people}}{84\text{ square miles}}\textsf{.}$ Cross-multiplying gives $84x = 37{,}800\textsf{,}$ so $x = 450\text{ people per mile}^{2}\textsf{.}$

Buzzer beatermedium

A metal sample has a mass of $540$ kilograms and a density of $12$ kilograms per cubic meter. What is the volume of the sample, in cubic meters?

Set up the proportion $\dfrac{12\text{ kilograms}}{1\text{ cubic meter}} = \dfrac{540\text{ kilograms}}{x\text{ cubic meters}}\textsf{.}$ Cross-multiplying gives $12x = 540\textsf{,}$ so $x = 45\text{ m}^{3}\textsf{.}$

Density from area and volume. Game on.

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