Prism/cylinder volume and capacity | Year 9

01 / LEARN

The idea, step by step

Layers make volume

A right prism or cylinder can be imagined as equal layers. Each layer has the same cross-sectional area. Multiplying that area by the perpendicular length or height counts the space in all layers. Use square units for the cross-section and cubic units for volume; a sloping edge is not a perpendicular height.

V = B L, V_{c y l i n d e r} = π r^{2} h

Volume and liquid capacity

One cubic centimetre holds one millilitre. A thousand cubic centimetres make one litre, while a cubic metre holds a thousand litres. For a partly full tank, use the water depth rather than the full tank height. Ignore wall thickness only when the question says to use internal dimensions.

1 {cm}^{3} = 1 mL, 1000 {cm}^{3} = 1 L, 1 m^{3} = 1000 L

A common trap

Treating 1 cubic metre as 100 litres because 1 metre is 100 centimetres.

Instead: Cubic conversion factors are cubed. One cubic metre is one million cubic centimetres, or 1000 litres.

02 / WORKED EXAMPLES

See the thinking

Example 1

A cylindrical container

Find the volume of a cylinder with internal radius 4 cm and height 10 cm. Give its capacity to the nearest millilitre.

$V = π (4^{2}) (10) = 160 π$ cm³.
$160 π \approx 502.65$ cm³, which is $502.65$ mL.
To the nearest millilitre the capacity is 503 mL.

160 π

cm³; approximately 503 mL.

Example 2

Find the water depth

A rectangular tank has an internal base 80 cm by 50 cm. It contains 40 L of water. Find the water depth.

$40$ L $= 40000$ cm³.
Base area $= 80 \times 50 = 4000$ cm².
$h = V / B = 40000 / 4000 = 10$ cm.

10 cm

Check your understanding

What is the capacity in litres of 2500 cm³?

Show answer

2.5 L.

Divide cubic centimetres by 1000 to obtain litres.

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find the volume of a rectangular prism 5 cm by 3 cm by 8 cm.
2 marks
A triangular prism has a cross-section with base 6 cm and perpendicular height 4 cm. Its length is 9 cm. Find its volume.
2 marks
A cylinder has radius 3 cm and height 20 cm. Give its exact volume and its capacity to the nearest millilitre.
3 marks
A rectangular tank has internal dimensions 0.8 m by 0.5 m by 0.4 m. Find its capacity in litres.
2 marks
A small pool is 2 m long, 1.5 m wide and 0.6 m deep. How many litres fill it?
2 marks
A tank has a 50 cm by 40 cm internal base. Find the water depth when it contains 13 L.
3 marks

Read the worked solutions

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

Find the volume of a rectangular prism 5 cm by 3 cm by 8 cm.
2 marks
$V = 5 \times 3 \times 8 = 120$ cm³.
120 cm³
A triangular prism has a cross-section with base 6 cm and perpendicular height 4 cm. Its length is 9 cm. Find its volume.
2 marks
$B = \frac{1}{2} (6) (4) = 12$ cm²; $V = 12 (9) = 108$ cm³.
108 cm³
A cylinder has radius 3 cm and height 20 cm. Give its exact volume and its capacity to the nearest millilitre.
3 marks
$V = π (3^{2}) (20) = 180 π$ cm³ $\approx 565.49$ cm³.
This is about 565 mL.
$180 π$ cm³; 565 mL.
A rectangular tank has internal dimensions 0.8 m by 0.5 m by 0.4 m. Find its capacity in litres.
2 marks
$V = 0.8 \times 0.5 \times 0.4 = 0.16$ m³.
$0.16 \times 1000 = 160$ L.
160 L
A small pool is 2 m long, 1.5 m wide and 0.6 m deep. How many litres fill it?
2 marks
$V = 2 \times 1.5 \times 0.6 = 1.8$ m³ $= 1800$ L.
1800 L
A tank has a 50 cm by 40 cm internal base. Find the water depth when it contains 13 L.
3 marks
$13$ L $= 13000$ cm³. Base area $= 2000$ cm².
$h = 13000 / 2000 = 6.5$ cm.
6.5 cm

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Curriculum reference & lesson scope

Australian Curriculum v9 / South Australian Curriculum

Year 9 surface area and volume of right prisms and cylinders, capacity, absolute/relative/percentage measurement error, precision and practical measurement problems.

Official curriculum source ↗

Back to Surface area, volume and measurement