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Density Calculations: Mass, Volume and Density — Answers

Answer sheet with model answers and success criteria for the Year 9 states of matter & materials worksheet.

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Success TutoringWorksheetsAnswer sheetYear 9 · Science · States of Matter & Materials

Density Calculations: Mass, Volume and Density — Answers

Part A: Calculating density

Density is the mass of a substance in a given volume: how tightly packed its matter is. Density = mass ÷ volume (D = m ÷ V). With mass in grams and volume in cm³, density is in g/cm³. Remember 1 mL = 1 cm³.

Volume of a box shape = length × width × height. For an irregular object, use displacement: lower it into water in a measuring cylinder; the rise in water level equals the object's volume.

Density table (g/cm³): cork 0.24 · ice 0.92 · water 1.0 · aluminium 2.7 · iron 7.9 · copper 9.0 · lead 11.3 · gold 19.3

1.A metal block has a mass of 54 g and a volume of 20 cm³. Calculate its density and use the table to identify the metal.

Answer: 2.7 g/cm³, aluminium

  1. D = m ÷ V = 54 ÷ 20 = 2.7 g/cm³
  2. This matches aluminium.
2.A wooden block measures 2 cm × 3 cm × 5 cm and has a mass of 18 g. Calculate its density.

Answer: 0.6 g/cm³

  1. V = 2 × 3 × 5 = 30 cm³
  2. D = 18 ÷ 30 = 0.6 g/cm³
3.Will the wooden block in the previous question float or sink in water? Explain.

Answer: It will float, because its density (0.6 g/cm³) is less than the density of water (1.0 g/cm³).

4.A small irregular metal object has a mass of 63.2 g. When it is lowered into a measuring cylinder, the water level rises from 50 mL to 58 mL. Calculate its density and identify the metal.

Answer: 7.9 g/cm³, iron

  1. Volume = 58 − 50 = 8 mL = 8 cm³
  2. D = 63.2 ÷ 8 = 7.9 g/cm³
  3. This matches iron.

Part B: Rearranging the formula

The formula can be rearranged: mass = density × volume and volume = mass ÷ density.

5.A gold ring has a volume of 5 cm³. What is its mass?

Answer: 96.5 g

  1. m = D × V
  2. m = 19.3 × 5 = 96.5 g
6.Ethanol has a density of 0.79 g/cm³. What volume does 158 g of ethanol occupy?

Answer: 200 cm³

  1. V = m ÷ D
  2. V = 158 ÷ 0.79 = 200 cm³
7.Densities are also given in kg/m³, where 1 g/cm³ = 1000 kg/m³. Write the density of aluminium in kg/m³.

Answer: 2700 kg/m³

  1. 2.7 × 1000 = 2700 kg/m³
8.A large block and a small block are cut from the same piece of copper. Which statement is correct?
  1. AThe large block has a greater density
  2. BThe small block has a greater density
  3. CBoth blocks have the same density
  4. DIt depends on the shape of each block

Answer: Both blocks have the same density

Density is a property of the substance. A bigger block has more mass, but also more volume, so the ratio stays the same.

Part C: Floating, sinking and particles

9.Using the table, which material would float in water?
  1. AAluminium
  2. BIce
  3. CLead
  4. DCopper

Answer: Ice

Ice (0.92 g/cm³) is less dense than water (1.0 g/cm³), so it floats. The metals are all denser than water and sink.

10.A heavy object always sinks and a light object always floats.

Answer: False

Floating depends on density, not mass alone. A huge log floats because its density is less than water's, while a tiny steel ball bearing sinks.

11.Use the particle model to explain why a gas is much less dense than the same substance as a solid.

Answer: In a gas the particles are very far apart, so there is much less mass in each cm³. In a solid the particles are packed closely together, so there is more mass in the same volume.

12.Most substances are densest as a solid, but ice floats on liquid water. What does this tell you about the spacing of water particles in ice?

Answer: In ice the water particles are held in an open arrangement that is more spread out than in liquid water, so ice is less dense than liquid water.

13.Oil (0.92 g/cm³), water (1.0 g/cm³) and syrup (1.4 g/cm³) are poured into a jar and do not mix. What is the order from top to bottom?
  1. ASyrup, water, oil
  2. BOil, water, syrup
  3. CWater, oil, syrup
  4. DOil, syrup, water

Answer: Oil, water, syrup

The least dense liquid floats on top and the densest sinks to the bottom.

14.When a metal rod is heated it expands, so its density decreases slightly.

Answer: True

Its mass stays the same but its volume increases, so mass ÷ volume becomes smaller.

Part D: Plan an investigation

15.You are given an irregular rock, a balance, a measuring cylinder and water. Write a method to find the density of the rock, and state one way to make your result more accurate.[4 marks]

Model answer: 1. Measure the mass of the rock on the balance and record it in grams. 2. Half-fill the measuring cylinder with water and record the volume, reading from the bottom of the meniscus at eye level. 3. Tilt the cylinder and gently slide the rock in so that it is fully covered and no water splashes out. 4. Record the new water level. 5. Volume of the rock = new level − starting level (in mL, which equals cm³). 6. Density = mass ÷ volume, in g/cm³. To improve accuracy, repeat the measurements several times and calculate an average, or use a narrower measuring cylinder with finer markings.

Success criteria:

  • Measures mass with the balance
  • Uses displacement to find the volume, subtracting the starting level
  • Calculates density as mass ÷ volume with correct units
  • Gives a valid way to improve accuracy (repeats, reading the meniscus at eye level, finer scale)
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