Density is an amount per unit of space: people per square mile, or grams per cubic centimeter. Divide the amount by the area or volume, or multiply back to find the amount.
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A rectangular park district is 9 miles by 9 miles and has 108,135 residents. Find its population density.
A town of 6,440 people covers 4 square miles. Find its population density.
A town of 680 people covers 4 square miles. Find its population density.
A rectangular park district is 9 miles by 8 miles and has 112,680 residents. Find its population density.
A town of 34,920 people covers 18 square miles. Find its population density.
A town of 9,050 people covers 5 square miles. Find its population density.
A rectangular park district is 8 miles by 3 miles and has 91,440 residents. Find its population density.
Find mass from density
A solid lead cylinder of radius 3 cm and height 12 cm has density 11.3 g/cm3. Find its mass to the nearest gram.
A silver bar is a box 1 cm by 2 cm by 11 cm. The density of silver is 10.5 g/cm3. Find its mass.
A solid iron cylinder of radius 4 cm and height 10 cm has density 7.9 g/cm3. Find its mass to the nearest gram.
A lead bar is a box 2 cm by 3 cm by 6 cm. The density of lead is 11.3 g/cm3. Find its mass.
A solid aluminum cylinder of radius 4 cm and height 12 cm has density 2.7 g/cm3. Find its mass to the nearest gram.
A solid copper cylinder of radius 1 cm and height 8 cm has density 9 g/cm3. Find its mass to the nearest gram.
A gold bar is a box 3 cm by 2 cm by 12 cm. The density of gold is 19.3 g/cm3. Find its mass.
Find density and decide if it floats
A toy has a volume of 108 cubic cm and a mass of 98 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).
A block 7 cm by 9 cm by 4 cm has a mass of 449 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).
A sealed jar has a volume of 432 cubic cm and a mass of 627 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).
A block 6 cm by 6 cm by 3 cm has a mass of 77 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).
An object has a volume of 504 cubic cm and a mass of 645 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).
A block 9 cm by 3 cm by 2 cm has a mass of 37 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).
A rectangular park district is 9 miles by 9 miles and has 108,135 residents. Find its population density.1,335 people per square mile
A town of 6,440 people covers 4 square miles. Find its population density.1,610 people per square mile
A town of 680 people covers 4 square miles. Find its population density.170 people per square mile
A rectangular park district is 9 miles by 8 miles and has 112,680 residents. Find its population density.1,565 people per square mile
A town of 34,920 people covers 18 square miles. Find its population density.1,940 people per square mile
A town of 9,050 people covers 5 square miles. Find its population density.1,810 people per square mile
A rectangular park district is 8 miles by 3 miles and has 91,440 residents. Find its population density.3,810 people per square mile
Find mass from density
A solid lead cylinder of radius 3 cm and height 12 cm has density 11.3 g/cm3. Find its mass to the nearest gram.3834 g
A silver bar is a box 1 cm by 2 cm by 11 cm. The density of silver is 10.5 g/cm3. Find its mass.231 g
A solid iron cylinder of radius 4 cm and height 10 cm has density 7.9 g/cm3. Find its mass to the nearest gram.3971 g
A lead bar is a box 2 cm by 3 cm by 6 cm. The density of lead is 11.3 g/cm3. Find its mass.406.8 g
A solid aluminum cylinder of radius 4 cm and height 12 cm has density 2.7 g/cm3. Find its mass to the nearest gram.1629 g
A solid copper cylinder of radius 1 cm and height 8 cm has density 9 g/cm3. Find its mass to the nearest gram.226 g
A gold bar is a box 3 cm by 2 cm by 12 cm. The density of gold is 19.3 g/cm3. Find its mass.1389.6 g
Find density and decide if it floats
A toy has a volume of 108 cubic cm and a mass of 98 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).0.91 g/cm3; it floats
A block 7 cm by 9 cm by 4 cm has a mass of 449 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).1.78 g/cm3; it sinks
A sealed jar has a volume of 432 cubic cm and a mass of 627 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).1.45 g/cm3; it sinks
A block 6 cm by 6 cm by 3 cm has a mass of 77 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).0.71 g/cm3; it floats
An object has a volume of 504 cubic cm and a mass of 645 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).1.28 g/cm3; it sinks
A block 9 cm by 3 cm by 2 cm has a mass of 37 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).0.69 g/cm3; it floats
A town of 12,000 people covers 8 square miles. Find its population density.
Density is people divided by area.
12,000 divided by 8.
The answer is 1,500 people per square mile.
Where students go wrong
Dividing the area by the population. Density puts the amount on top and the space on the bottom.
Also called population density, mass and density, density problems or modeling with density.
What you can put on this worksheet
Population density
A town of 67,620 people covers 23 square miles. Find its population density.→ 2,940 people per square mile
Mass and density
A lead bar is a box 4 cm by 2 cm by 12 cm. The density of lead is 11.3 g/cm3. Find its mass.→ 1084.8 g
Density and floating
A block 6 cm by 7 cm by 8 cm has a mass of 140 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).→ 0.42 g/cm3; it floats
Questions about these worksheets
Yes. Every density sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the density questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 3: population density, mass and density and density and floating. Tick as many as you want and set how many of each, or let it spread them evenly.
Dividing the area by the population. Density puts the amount on top and the space on the bottom.