Volume and Liquid Displacement

What you’ll learn

Measure regular and irregular volumes.

វាស់មាឌវត្ថុរាងទៀងទាត់ និងវត្ថុរាងមិនទៀងទាត់។

Meaning and use

A cuboid’s volume is the product of three perpendicular dimensions. An irregular solid can be measured by the rise of liquid in a measuring cylinder if it is fully immersed and does not dissolve, absorb liquid, or trap air. Read the scale carefully and use a suitable meniscus convention.

មាឌប្រអប់កែងស្មើបណ្ដោយគុណទទឹងគុណកម្ពស់។ វត្ថុមិនទៀងទាត់អាចវាស់តាមមាឌទឹកកើន បើលិចទាំងស្រុង និងមិនរលាយ ឬស្រូបទឹក។

Formulas

Cuboid volume

\[V=lwh\]

Displacement volume

\[V_{\mathrm{solid}}=V_{\mathrm{final}}-V_{\mathrm{initial}}\]

Symbols and units

Symbol	Meaning	Unit or restriction
V	Volume	m³ or cm³
l, w, h	Perpendicular cuboid dimensions	Same length unit
Vinitial, Vfinal	Liquid readings before and after immersion	mL or cm³

Conditions and limits

• For displacement, the whole solid must be below the liquid surface.
• The measurement assumes no significant dissolution, absorption, spilling, or trapped air.
• 1 mL = 1 cm³; use the scale’s resolution honestly.

Worked examples

Regular solid

A block is 4 cm by 3 cm by 2 cm.

1. Use \(V=lwh\).
2. Calculate \(4\times3\times2=24\) cm³.

24 cm³

គុណប្រវែងទាំងបីដែលកែងគ្នា។

An immersed stone

The cylinder rises from 40 mL to 58 mL.

1. Subtract initial from final.
2. Calculate \(58-40=18\) mL.
3. Use \(1\,\mathrm{mL}=1\,\mathrm{cm^3}\).

18 cm³

មាឌវត្ថុស្មើមាឌទឹកដែលបានជំនួស។

Common mistakes

Instead of	Use	Why
The stone volume is the final liquid reading.	It is final minus initial reading.	Subtract the liquid already present.
24 cm³ is an area.	24 cm³ is a volume.	Cubic units measure volume.

Practice

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

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. A block is 5 cm × 2 cm × 3 cm. Find its volume.
2. Water rises from 65 to 80 mL. Find displaced volume.
3. Why is a floating object unsuitable for this full-immersion measurement without an extra method?

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 30 cm³

   Multiply all three perpendicular dimensions.

2. 15 cm³

   80 − 65 = 15 mL = 15 cm³.

3. Only part of its volume is submerged.

   The rise alone would not give its entire volume.

Quick recap

• Use three perpendicular dimensions for a cuboid.
• Subtract initial liquid volume.
• Check the full-immersion assumptions.