Density, mass and volume

A supplied record labels mass as 12 g and volume as 9 cm³. Which quantity is the mass?

Use the label and unit rather than choosing the larger number automatically

Measure mass and the corresponding volume

Mass is a measure of the amount of matter in a sample and can be measured using a balance, commonly in grams or kilograms. Volume is the space occupied, commonly in millilitres or cubic centimetres

A cubic centimetre is the volume of a cube with edges one centimetre long. Centimetres without the cube measure length, not volume

Density is mass per unit volume. A density of 3 grams per cubic centimetre means that each cubic centimetre of a uniform material contains 3 grams under the stated conditions

Do not confuse density with total mass, viscosity or how dark a material looks. A larger sample can have more mass without being denser

A supplied table or drawing is evidence only for its stated measurements and key. It does not by itself establish a real material's identity or measure individual particles

Find the amount in one unit of volume

To find mass in one cubic centimetre, divide the total mass by the number of cubic centimetres. Division answers how much mass belongs to each equal unit of volume

For an original example, 30 g occupying 10 cm³ gives 3 g for each cubic centimetre

For equal volumes, greater mass means greater density. For equal masses, smaller volume means greater density. When both differ, compare their mass-per-volume ratios rather than only the masses

For uniform samples of one unchanged material at the same temperature and pressure, increasing the amount increases mass and volume together without changing density. Cavities or mixed composition need separate consideration

Predict whether the largest sample will be denser, then inspect all three supplied records. These uniform samples have the same composition, temperature and pressure and no cavities. The selector displays records, not a simulation or a new measurement. Compare the mass with its corresponding volume in each record

What stays the same across these records?

Compare equal volumes

Compare equal masses

Distinguish amount from density

Use compatible mass and volume units

One millilitre is exactly one cubic centimetre. A reading of 23 mL is therefore 23 cm³, not 23 cm

If the requested density is in grams per cubic centimetre, convert a kilogram mass to grams first by multiplying by 1000. For example, 0.036 kg is 36 g

The slash in g/cm³ means grams per cubic centimetre. Grams alone are not a density unit, and changing a unit label without converting its number changes the stated quantity

Use the simple given values in this lesson without rounding intermediate steps. Real measurements have limited precision; extra calculator digits do not create more precise measurements

Keep the cubic volume unit

Divide mass by volume

A uniform sample has mass 63 g and volume 21 cm³. Use density equal to mass divided by volume

Calculate the density and explain why the answer needs a mass-per-volume unit

Density is the 63 g mass divided by the corresponding 21 cm³ volume

63 divided by 21 is 3, so the density is 3 g/cm³ rather than 3 g

Convert before dividing

Find the sample's volume, not the container reading

A liquid's volume can be read from a suitable measuring cylinder. Use the scale and an appropriate eye-level reading; for water, read the bottom of the curved surface called the meniscus

A fully submerged solid can displace its own volume of water if it does not dissolve, react, absorb water or trap bubbles. Use the increase from the initial to final reading, not the final total alone

For a regular rectangular solid, measured length times width times height gives its external volume. The geometry and dimensions must actually fit that method; a photograph alone is not a measurement

Use the sample mass without the container's mass, and pair it with the same sample's volume. Any practical method needs suitable materials, equipment and teacher supervision; these questions use supplied records

Use the change in the water reading

Recover mass or volume from the same relationship

If each cubic centimetre contains a known mass, multiply by the number of cubic centimetres to find the total mass

For volume, ask how many unit-volume groups fit the total mass. A sample with 35 g and density 5 g/cm³ contains seven groups of 5 g, so it occupies 7 cm³

These relations are the same mass-per-volume idea, not three unrelated formulas. Keep the quantity being found and its unit together

Use the mass in each cubic centimetre

A uniform sample has mass 36 g and density 4 g/cm³ under the stated conditions. What is its volume?

Find how many 4 g groups fit into 36 g; each such group occupies one cubic centimetre

Connect density to a complete particle key

A particle explanation of density depends on both the mass of the particles and their arrangement. Different substances can have different particle masses as well as different spacing

Within equal represented volumes, more equal-mass particles mean greater represented mass and density. If particle masses, volume scales or the meaning of the counts differ or are unknown, circle count alone cannot decide density

A drawing usually shows a selected set of particles, not every real particle. Use its stated scale and key; colour and drawn circle size do not measure particle mass

Use the supplied equal-mass key

Density can change when conditions change

If a fixed mass expands, the same mass occupies more volume and density decreases. If it is compressed into less volume, density increases

Many materials expand when warmed under suitable conditions, but there are exceptions and fixed boundaries. Use the observed volume change rather than assuming all warmer samples expand

In the particle model, changed average spacing can change sample volume without each particle growing. A change in a sample's density is not evidence that its individual particles gain or lose mass

Record temperature and, especially for gases, pressure when comparing densities. A reference value at one condition is not automatically the value at every condition

Explain a measured density trend

Check the method and the claim

If a correct mass is divided by a volume that is too large, the calculated density is too small. For example, dividing 20 g by 10 cm³ gives 2 g/cm³, whereas incorrectly using 20 cm³ gives only 1 g/cm³

Trapped air bubbles can make a displacement rise too large. Repeating the same flawed method does not automatically remove that error; the cause needs to be addressed

A matching density can help narrow possible materials but need not identify a unique substance. Different materials may have similar densities, mixtures also have densities, and measurement uncertainty and conditions matter

For a hollow or porous object, state whether the volume includes cavities. Average density of the whole object is not necessarily the density of the solid material alone

Follow a stated volume error

Keep identification within the evidence

Construct a comparison and evaluate a model

Written and calculation task, not automatically marked

Two uniform samples at the same temperature and pressure have these supplied records: A has mass 36 g and volume 12 cm³; B has mass 80 g and volume 20 cm³. Neither sample has cavities

An unscaled model is described as showing five circles for A and eight for B but gives no particle-mass key or represented-volume scale. No other identification evidence is supplied

Before reading the model, calculate both densities with units, identify the denser sample and explain why comparing masses alone is not enough. State whether that description independently establishes that comparison and whether density alone uniquely identifies either material

Check the ratios and the limits

Here the symbol rho names density. B is denser because 4 grams per cubic centimetre exceeds 3, not just because B has greater total mass; the sample volumes also differ

The described model lacks particle masses and represented volumes, so its circle counts cannot independently establish density. The complete mass-volume measurements support the comparison

Neither density alone uniquely identifies a material or proves purity. Further suitable evidence would be needed, with conditions and measurement limits considered

Review quantity, calculation and evidence

Density is mass per unit volume. Equal-volume and equal-mass comparisons are useful shortcuts only when their stated conditions hold

Pair the same sample's mass and volume, convert units as needed and use the volume increase for valid displacement records. Keep the answer's unit with the quantity being found

Density depends on composition and conditions, not simply total sample size. Particle keys and measurements need enough information, and a density match is not automatically a unique identification