Volume and capacity | Year 11

01 / LEARN

The idea, step by step

Understand the idea

A prism has a constant cross-section. Its volume equals cross-sectional area multiplied by perpendicular length. The cylinder is the same idea with a circular cross-section.

Capacity concerns the interior. Outside dimensions may overstate the contents if walls have significant thickness. A tank that is partly full contains only the stated fraction of its full internal volume.

Choose and apply a method

Find cross-sectional area first, including its square unit. Multiply by prism length to obtain cubic units. For a triangular cross-section use a perpendicular triangle height.

Convert capacity after the volume calculation. Keep exact expressions involving $π$ until the final rounding step. Check whether the result is a whole-container volume or a stated amount of liquid.

V_{prism} = A_{cross-section} L, V_{cylinder} = π r^{2} h

A common trap

Putting the cylinder diameter in place of its radius.

Instead: Halve the diameter first; using double the radius makes the volume four times too large.

02 / WORKED EXAMPLES

See the thinking

Example 1

Triangular prism

A triangular prism has cross-section base 6 cm, perpendicular height 4 cm and length 10 cm. Find volume.

Cross-sectional area $= \frac{1}{2} \times 6 \times 4 = 12$ cm $2$ .
Volume $= 12 \times 10 = 120$ cm $3$ .

120 cm

3

Example 2

Tank capacity

A tank has internal radius 0.5 m and height 1.2 m. Find its capacity to the nearest litre.

$V = π {(0.5)}^{2} (1.2) = 0.3 π$ m $3$ .
Convert to $300 π \approx 942.48$ L.
Round to 942 L.

942 L.

Check your understanding

A container has internal volume 0.35 m $3$ . Find capacity.

Show answer

350 L.

$0.35 \times 1000 = 350$ .

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find volume of a 7 cm by 5 cm by 4 cm cuboid.
2 marks
A prism cross-section has area 18 cm $2$ and length 12 cm. Find volume.
2 marks
A triangular prism has cross-section base 8 cm, perpendicular height 3 cm and length 9 cm. Find volume.
2 marks
A cylinder has diameter 6 cm and height 10 cm. Find exact volume.
2 marks
An internal tank 1.5 m by 0.8 m by 0.6 m is 75% full. Find water volume in litres.
2 marks
A cylinder has volume $200 π$ cm $3$ and radius 5 cm. Find height.
2 marks

Read the worked solutions

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

Find volume of a 7 cm by 5 cm by 4 cm cuboid.
2 marks
$7 \times 5 \times 4 = 140$ .
140 cm $3$ .
A prism cross-section has area 18 cm $2$ and length 12 cm. Find volume.
2 marks
$18 \times 12 = 216$ .
216 cm $3$ .
A triangular prism has cross-section base 8 cm, perpendicular height 3 cm and length 9 cm. Find volume.
2 marks
$(\frac{1}{2} \times 8 \times 3) \times 9 = 108$ .
108 cm $3$ .
A cylinder has diameter 6 cm and height 10 cm. Find exact volume.
2 marks
Radius $= 3$ cm.
$V = π {(3)}^{2} (10) = 90 π$ .
$90 π$ cm $3$ .
An internal tank 1.5 m by 0.8 m by 0.6 m is 75% full. Find water volume in litres.
2 marks
Full volume $= 0.72$ m $3 = 720$ L.
$0.75 \times 720 = 540$ L.
540 L.
A cylinder has volume $200 π$ cm $3$ and radius 5 cm. Find height.
2 marks
$200 π = π {(5)}^{2} h = 25 π h$ .
$h = 8$ cm.
8 cm.

Checking saved progress…

Continue learning

Practical measurement models

Next lesson

Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics measurement skills and applications; original explanatory lessons and papers.

Official curriculum source ↗

Back to Measurement