Volumes of Prisms and Cylinders

What you’ll learn

Calculate volume from a constant cross-sectional area.

គណនាមាឌដោយផ្ទៃកាត់ថេរ និងប្រវែង។

Meaning and use

A prism has the same cross-sectional area along its length. Multiplying that area by the perpendicular length gives volume. A right circular cylinder uses a circular base. Volume uses cubic units; capacity can be converted using one litre equals one thousand cubic centimetres.

ព្រីសមានផ្ទៃកាត់ដូចគ្នាតាមបណ្ដោយ។ មាឌស្មើផ្ទៃកាត់គុណប្រវែងកែង។ ស៊ីឡាំងរង្វង់ត្រង់ប្រើបាតរង្វង់ ហើយមាឌមានឯកតាគូប។

Formulas

Constant cross-section

\[V=AL\]

Right circular cylinder

\[V=\pi r^2 h\]

Symbols and units

Symbol	Meaning	Unit or restriction
V	Volume	cm³ or m³
A	Cross-sectional area	cm² or m²
L, h	Perpendicular length or height	Matching length unit
r	Cylinder radius	Same length unit as h

Conditions and limits

• The cross-section must remain constant for V = AL.
• Use radius, not diameter, in the cylinder formula.
• 1 L = 1000 cm³; do not confuse area and volume conversions.

Worked examples

A rectangular prism

Length 5 cm, width 4 cm, height 3 cm.

1. Base area \(A=5\times4=20\) cm².
2. Volume \(V=20\times3=60\) cm³.

60 cm³

គុណផ្ទៃបាតនឹងកម្ពស់ ដើម្បីបានឯកតាគូប។

A cylinder

Radius 2 cm, height 5 cm.

1. Base area \(A=\pi\times2^2=4\pi\) cm².
2. Volume \(V=4\pi\times5=20\pi\) cm³.

\(20\pi\,\mathrm{cm^3}\)

កាំត្រូវលើកការ៉េ មុនគុណ π និងកម្ពស់។

Common mistakes

Instead of	Use	Why
Volume is measured in cm².	Volume is measured in cm³.	Volume has three length dimensions.
Use cylinder diameter directly in πr²h.	Halve the diameter to get r first.	The formula uses radius.

Practice

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

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. A prism has cross-section 12 cm² and length 7 cm. Find volume.
2. A cylinder has r = 3 m and h = 2 m. Leave pi exact.
3. Convert 2500 cm³ to litres.

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 84 cm³

   12 × 7 = 84.

2. 18π m³

   π × 3² × 2 = 18π.

3. 2.5 L

   Divide by 1000.

Quick recap

• Volume equals cross-section times perpendicular length.
• Use cubic units.
• Convert capacity with the correct scale factor.