Prism volume and capacity | Year 8

01 / LEARN

The idea, step by step

Build volume from area

For a prism, $V = A L$ , where $A$ is a repeated cross-sectional area and $L$ is the perpendicular distance between the matching ends. For a cylinder, the cross-section is a circle, so $V = π r^{2} h$ .

Use one length unit consistently. A cross-sectional area in cm² multiplied by a length in cm gives cm³. Multiplying area by another area would not give volume.

V = A L

Connect volume and capacity

Capacity describes how much a container can hold. One cubic centimetre holds 1 mL, and 1000 cm³ holds 1 L. One cubic metre holds 1000 L. These relationships apply to the inside dimensions of a container.

A tank’s outside dimensions can overestimate capacity when walls are thick. Unless a problem says otherwise, use the supplied internal dimensions for a capacity calculation.

Volume and capacity
Volume	Capacity
1 cm³	1 mL
1000 cm³	1 L
1 m³	1000 L

A common trap

Multiplying a cylinder’s circumference by its height to find volume.

Instead: Use the area of the circular cross-section, $π r^{2}$ , then multiply by height.

02 / WORKED EXAMPLES

See the thinking

Example 1

A triangular prism

A triangular prism has cross-section base 6 cm, perpendicular height 4 cm and length 9 cm. Find its volume.

End area: $A = \frac{1}{2} (6) (4) = 12$ cm².
Multiply by prism length: $V = 12 (9) = 108$ cm³.

108 cm³.

Example 2

A cylinder

A cylindrical container has internal radius 3 cm and height 7 cm. Find its volume exactly and its capacity in mL.

Circle area: $A = π {(3)}^{2} = 9 π$ cm².
Volume: $V = 9 π (7) = 63 π$ cm³.
Because 1 cm³ equals 1 mL, the capacity is $63 π$ mL.

63 π

cm³, equivalent to

63 π

mL.

Check your understanding

A prism has cross-sectional area 12 cm² and length 5 cm. What is its volume?

Show answer

60 cm³.

$V = 12 (5) = 60$ cm³.

03 / WORKSHEET

Your turn

6 questions · 15 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find the volume of a rectangular prism 8 cm by 3 cm by 2 cm.
2 marks
A prism has cross-sectional area 15 m² and length 4 m. Find its volume.
2 marks
A triangular prism has cross-section base 10 cm, perpendicular height 6 cm and length 8 cm. Find its volume.
3 marks
Find the volume of a cylinder with radius 2 m and height 5 m.
2 marks
A container holds 3500 cm³. Express its capacity in litres.
2 marks
A rectangular tank holds 240 L. Its internal base is 0.8 m by 0.5 m. Find its internal height.
4 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Find the volume of a rectangular prism 8 cm by 3 cm by 2 cm.
2 marks
$V = 8 (3) (2) = 48$ cm³.
48 cm³.
A prism has cross-sectional area 15 m² and length 4 m. Find its volume.
2 marks
$V = 15 (4) = 60$ m³.
60 m³.
A triangular prism has cross-section base 10 cm, perpendicular height 6 cm and length 8 cm. Find its volume.
3 marks
Cross-sectional area is $\frac{1}{2} (10) (6) = 30$ cm².
Volume is $30 (8) = 240$ cm³.
240 cm³.
Find the volume of a cylinder with radius 2 m and height 5 m.
2 marks
$V = π {(2)}^{2} (5) = 20 π$ m³.
$20 π$ m³.
A container holds 3500 cm³. Express its capacity in litres.
2 marks
$3500 \div 1000 = 3.5$ L.
3.5 L.
A rectangular tank holds 240 L. Its internal base is 0.8 m by 0.5 m. Find its internal height.
4 marks
240 L is 0.24 m³.
Base area is $0.8 (0.5) = 0.4$ m².
Height is $0.24 / 0.4 = 0.6$ m.
0.6 m.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Circumference and area of circles; perimeter/area of composite shapes; choosing and converting area units; cross-sections of prisms; prism volume and capacity; mixed measurement applications.

Official curriculum source ↗

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