The Life Starter
Sign up
Grade 10 · lesson 3 of 4

Interpret Mass per Unit Volume

Density compares total mass with occupied volume.

About 20 minutes, plus any extended practice

Download the grade pack

Supplied materials

  • Paper or a browser scratch area; a calculator is optional unless rounding is requested.
  • Supplied teaching case: A fictional uniform block has mass 24 grams and volume 6 cm³. Find its density. Candidate answers: (A) 1/4 g/cm³ (B) 144 g/cm³ (C) 24 g/cm³ (D) 4 g/cm³.
  • Independent check inputs: A fictional uniform block has mass 45 grams and volume 9 cm³. Find its density. Candidate answers: (A) 1/5 g/cm³ (B) 405 g/cm³ (C) 45 g/cm³ (D) 5 g/cm³.

Learn the idea

Geometry can support probability, material, density and layout models when the assumptions are explicit. Ratios and decompositions must use nonoverlapping regions, consistent dimensions and the correct uniformity or exact-fit conditions. Density compares total mass with occupied volume. A supplied uniform-block model uses one constant mass-per-volume ratio, allowing the ratio to be calculated from its complete measurements.

Here is the method on the supplied teaching case. Density=mass/volume=24/6=4 g/cm³. The ratio names mass in one cubic centimeter, not the block’s total mass.

Dividing volume by mass gives a reciprocal unit and a different quantity. Label both inputs before calculating; a uniform fictional block does not establish the density of all real materials.

  1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
  2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
  3. Solve the independent check with its changed inputs before revealing feedback.
  4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
Worked example

See the method in action

Teaching case: A fictional uniform block has mass 24 grams and volume 6 cm³. Find its density. Candidate answers: (A) 1/4 g/cm³ (B) 144 g/cm³ (C) 24 g/cm³ (D) 4 g/cm³. Solution: Density=mass/volume=24/6=4 g/cm³. The ratio names mass in one cubic centimeter, not the block’s total mass. The final answer is 4 g/cm³. Dividing volume by mass gives a reciprocal unit and a different quantity. Label both inputs before calculating; a uniform fictional block does not establish the density of all real materials.

Your turn

Check your reasoning

Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.

Helpful tips
  • Density compares total mass with occupied volume.
  • Dividing volume by mass gives a reciprocal unit and a different quantity.
A fictional uniform block has mass 45 grams and volume 9 cm³. Find its density.

Feedback appears here after you check. This is practice, not a graded school assessment.

See the answer and explanation

5 g/cm³

Density=mass/volume=45/9=5 g/cm³. The ratio names mass in one cubic centimeter, not the block’s total mass.

Take it further

Changed-input task: A fictional uniform block has mass 297 grams and volume 27 cm³. Find its density. Candidate answers: (A) 1/11 g/cm³ (B) 11 g/cm³ (C) 297 g/cm³ (D) 8019 g/cm³. Show the mathematical reason, not only the selected answer. Expected result: 11 g/cm³. Density=mass/volume=297/27=11 g/cm³. The ratio names mass in one cubic centimeter, not the block’s total mass.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.

More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

More practice: try new cases
1. A fictional uniform block has mass 72 grams and volume 12 cm³. Find its density.
Need a hint?
  • Density compares total mass with occupied volume.
  • Dividing volume by mass gives a reciprocal unit and a different quantity.
2. A fictional uniform block has mass 105 grams and volume 15 cm³. Find its density.
Need a hint?
  • Density compares total mass with occupied volume.
  • Dividing volume by mass gives a reciprocal unit and a different quantity.
3. A fictional uniform block has mass 144 grams and volume 18 cm³. Find its density.
Need a hint?
  • Density compares total mass with occupied volume.
  • Dividing volume by mass gives a reciprocal unit and a different quantity.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

Check the subject sources

These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.