Worksheets · Geometry

Density worksheet

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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Pick more than one for a sheet that mixes them.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Density

Date Period

Answer each question.

  1. A rectangular park district is 9 miles by 9 miles and has 108,135 residents. Find its population density.
  2. 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.
  3. A block 6 cm by 6 cm by 3 cm has 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).
  4. A town of 15,840 people covers 8 square miles. Find its population density.
  5. A gold bar is a box 4 cm by 3 cm by 8 cm. The density of gold is 19.3 g/cm3. Find its mass.
  6. A block 2 cm by 5 cm by 7 cm has a mass of 105 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).
  7. A town of 26,500 people covers 10 square miles. Find its population density.
  8. A solid iron cylinder of radius 5 cm and height 4 cm has density 7.9 g/cm3. Find its mass to the nearest gram.
  9. A block 8 cm by 3 cm by 4 cm has a mass of 88 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).
  10. A town of 20,440 people covers 7 square miles. Find its population density.
  11. A lead bar is a box 2 cm by 2 cm by 14 cm. The density of lead is 11.3 g/cm3. Find its mass.
  12. A block 9 cm by 4 cm by 10 cm has a mass of 496 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).
  13. A town of 35,490 people covers 13 square miles. Find its population density.
  14. A solid copper cylinder of radius 4 cm and height 12 cm has density 9 g/cm3. Find its mass to the nearest gram.
  15. A block 9 cm by 10 cm by 3 cm has a mass of 97 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).
  16. A rectangular park district is 9 miles by 6 miles and has 172,800 residents. Find its population density.
  17. A solid gold cylinder of radius 5 cm and height 3 cm has density 19.3 g/cm3. Find its mass to the nearest gram.
  18. A block 10 cm by 3 cm by 5 cm has a mass of 71 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).
  19. A town of 37,100 people covers 14 square miles. Find its population density.
  20. A solid lead cylinder of radius 1 cm and height 10 cm has density 11.3 g/cm3. Find its mass to the nearest gram.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

DensityAnswer keyVersion 1

Date Period

Answer each question.

  1. 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
  2. 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
  3. A block 6 cm by 6 cm by 3 cm has 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
  4. A town of 15,840 people covers 8 square miles. Find its population density.1,980 people per square mile
  5. A gold bar is a box 4 cm by 3 cm by 8 cm. The density of gold is 19.3 g/cm3. Find its mass.1852.8 g
  6. A block 2 cm by 5 cm by 7 cm has a mass of 105 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).1.50 g/cm3; it sinks
  7. A town of 26,500 people covers 10 square miles. Find its population density.2,650 people per square mile
  8. A solid iron cylinder of radius 5 cm and height 4 cm has density 7.9 g/cm3. Find its mass to the nearest gram.2482 g
  9. A block 8 cm by 3 cm by 4 cm has a mass of 88 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).0.92 g/cm3; it floats
  10. A town of 20,440 people covers 7 square miles. Find its population density.2,920 people per square mile
  11. A lead bar is a box 2 cm by 2 cm by 14 cm. The density of lead is 11.3 g/cm3. Find its mass.632.8 g
  12. A block 9 cm by 4 cm by 10 cm has a mass of 496 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).1.38 g/cm3; it sinks
  13. A town of 35,490 people covers 13 square miles. Find its population density.2,730 people per square mile
  14. A solid copper cylinder of radius 4 cm and height 12 cm has density 9 g/cm3. Find its mass to the nearest gram.5429 g
  15. A block 9 cm by 10 cm by 3 cm has a mass of 97 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).0.36 g/cm3; it floats
  16. A rectangular park district is 9 miles by 6 miles and has 172,800 residents. Find its population density.3,200 people per square mile
  17. A solid gold cylinder of radius 5 cm and height 3 cm has density 19.3 g/cm3. Find its mass to the nearest gram.4547 g
  18. A block 10 cm by 3 cm by 5 cm has a mass of 71 g. Find its density to the nearest hundredth, and say whether it floats in water (density 1 g per cubic cm).0.47 g/cm3; it floats
  19. A town of 37,100 people covers 14 square miles. Find its population density.2,650 people per square mile
  20. A solid lead cylinder of radius 1 cm and height 10 cm has density 11.3 g/cm3. Find its mass to the nearest gram.355 g

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

A town of 12,000 people covers 8 square miles. Find its population density.

  1. Density is people divided by area.
  2. 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.