Mass, Volume, and Density

What you’ll learn

Calculate density and rearrange its relationship.

គណនាម៉ាសមាឌ និងប្ដូររូបមន្តដើម្បីរកម៉ាសឬមាឌ។

Meaning and use

Density is mass per unit volume. Mass is measured with a balance; volume describes occupied space. Use consistent units, such as kilograms and cubic metres or grams and cubic centimetres. Density can vary with temperature and material composition, so a calculated value is tied to its measurement conditions.

ម៉ាសមាឌជាម៉ាសក្នុងមួយឯកតាមាឌ។ ប្រើឯកតាស្របគ្នា ដូច kg ជាមួយ m³ ឬ g ជាមួយ cm³។ ម៉ាសមាឌអាចប្រែប្រួលតាមសីតុណ្ហភាព និងសមាសភាព។

Formulas

Density and rearrangements

\[\rho=\frac mV,\qquad m=\rho V,\qquad V=\frac m\rho\]

Unit conversion

\[1\,\mathrm{g/cm^3}=1000\,\mathrm{kg/m^3}\]

Symbols and units

Symbol	Meaning	Unit or restriction
ρ	Density	kg/m³ or g/cm³
m	Mass	kg or g matching density units
V	Volume	m³ or cm³ matching density units

Conditions and limits

• Volume must be positive.
• For a mixed or hollow object, the calculated average density depends on which volume is used.
• កុំច្រឡំម៉ាសជាមួយទម្ងន់ដែលជាកម្លាំង។

Worked examples

Finding density

A block has mass 60 g and volume 20 cm³.

1. Use \(\rho=m/V\).
2. Calculate \(60/20=3\) g/cm³.

3 g/cm³

ឯកតាម៉ាស និងមាឌត្រូវស្របនឹងឯកតាម៉ាសមាឌដែលចង់បាន។

Finding mass

A material has density 800 kg/m³ and volume 0.02 m³.

1. Use \(m=\rho V\).
2. Calculate \(800\times0.02=16\) kg.

16 kg

រូបមន្តប្ដូរដោយគុណម៉ាសមាឌនិងមាឌ។

Common mistakes

Instead of	Use	Why
Density = volume / mass.	Density = mass / volume.	The definition is mass per unit volume.
1 g/cm³ = 1 kg/m³.	1 g/cm³ = 1000 kg/m³.	Both mass and cubic-volume conversions matter.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Mass 100 g, volume 25 cm³: find density.
2. Density 2 g/cm³, volume 15 cm³: find mass.
3. Mass 50 g, density 5 g/cm³: find volume.

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 4 g/cm³

   100/25 = 4.

2. 30 g

   2 × 15 = 30.

3. 10 cm³

   50/5 = 10.

Quick recap

• Density is mass divided by volume.
• Match units before substituting.
• Mass and weight are different quantities.