Year 8 - Volume - Free practice

Year 8 Volume Worksheets & Practice Tests

Right prisms, capacity, real-world volume problems.

Quick answer

How do you find the volume of a right prism?

Multiply the area of the cross-sectional face by the length (or height) of the prism: V = A × l. First find the area of the base shape (rectangle, triangle, trapezium, etc.), then multiply by how far the prism extends. For example, a triangular prism with base area 12 cm² and length 5 cm has volume 60 cm³.

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Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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Worked examples

Year 8 volume: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Volume of a triangular prism
A triangular prism has a right-angled triangular cross-section with base $6$ cm and perpendicular height $4$ cm. The prism is $10$ cm long. Find its volume.
Show worked solution
Key idea: The volume of any right prism is $V = A_{\text{cross-section}} \times \text{length}$ .
1. Find the area of the triangular cross-section:
  $A = \frac{1}{2} \times base \times height = \frac{1}{2} \times 6 \times 4 = 12 \text{ cm}^2$
2. Multiply by the length of the prism:
  $V = 12 \times 10 = 120 \text{ cm}^3$
Answer: $120 \text{ cm}^3$
Example 2 · Volume of a trapezoidal prism
A trapezoidal prism has a cross-section that is a trapezium with parallel sides of $5$ cm and $9$ cm, and a perpendicular height of $6$ cm. The prism has a length of $12$ cm. Find its volume.
Show worked solution
Key idea: Find the area of the trapezoidal cross-section first, then multiply by the length.
1. Find the area of the trapezoidal cross-section:
  $A = \frac{1}{2}(a + b) \times h = \frac{1}{2}(5 + 9) \times 6 = \frac{1}{2} \times 14 \times 6 = 42 \text{ cm}^2$
2. Multiply by the length of the prism:
  $V = 42 \times 12 = 504 \text{ cm}^3$
Answer: $504 \text{ cm}^3$
Example 3 · Capacity of a swimming pool
A swimming pool has a cross-section that is a trapezium. The pool is $1.2$ m deep at the shallow end and $2.0$ m deep at the deep end. The pool is $25$ m long and $10$ m wide. Water is filled to the top. How many litres of water does the pool hold? ( $1 \text{ m}^3 = 1000 \text{ L}$ )
Show worked solution
Key idea: Model the pool as a trapezoidal prism. Find the volume in cubic metres, then convert to litres.
1. Find the area of the trapezoidal cross-section (the side face, length $\times$ depth):
  $A = \frac{1}{2}(d_1 + d_2) \times l = \frac{1}{2}(1.2 + 2.0) \times 25 = \frac{1}{2} \times 3.2 \times 25 = 40 \text{ m}^2$
2. Multiply by the width to get the volume:
  $V = 40 \times 10 = 400 \text{ m}^3$
3. Convert to litres:
  $400 \times 1000 = 400\,000 \text{ L}$
Answer: $400\,000$ L

Common mistakes

Where students usually lose marks

Using the wrong area formula for the cross-section

Area of trapezium $= (a + b) \times h$ (forgetting to halve)

The correct formula is $A = \frac{1}{2}(a + b) \times h$ . Always write the formula in full before substituting numbers, so you do not accidentally leave out the $\frac{1}{2}$ .

Multiplying the wrong dimension by the cross-section area

Finding the area of a face that is not the cross-section, then multiplying by an incorrect dimension

Always identify the cross-section (the shape that stays the same all the way along the prism) first. The length you multiply by must be the dimension going perpendicular to that cross-section.

Forgetting to convert units before calculating

Mixing cm and m in the same calculation, e.g. $V = 40 \times 10 \text{ cm}$ when the other dimensions are in metres

Convert all lengths to the same unit before you start. If the answer needs to be in cm $^3$ , convert everything to cm first; if in m $^3$ , convert everything to m.

Incorrect capacity conversion

$1 \text{ m}^3 = 100 \text{ L}$ or $1 \text{ cm}^3 = 10 \text{ mL}$

Remember: $1 \text{ cm}^3 = 1 \text{ mL}$ , $1000 \text{ cm}^3 = 1 \text{ L}$ , and $1 \text{ m}^3 = 1000 \text{ L}$ . Write these conversions at the top of your working as a reminder.

Try one yourself

Your turn

A trapezoidal prism has a cross-section with parallel sides of $6$ cm and $10$ cm and a perpendicular height of $4$ cm. The prism is $9$ cm long. Find the volume of the prism in cm³.

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About this worksheet

Why we built it

Year 8 builds on the Year 7 volume formula and adds capacity (litres) and a wider range of prism cross-sections. These worksheets give your student practice in both directions - calculating volume from dimensions, and working back to find a missing dimension when the volume is known.

What's covered

Sub-skills your student will practise

✓Volume of rectangular and triangular prisms
✓Volume of trapezoidal and other right prisms
✓Capacity (mL, L, kL) conversions
✓Working back from volume to find a missing dimension
✓Composite-prism problems (steps, swimming pools)

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Frequently asked

Questions parents ask about volume

What's new about Year 8 volume compared to Year 7?

Year 8 adds capacity (mL, L, kL conversions), trapezoidal and other non-rectangular cross-sections, and working back from a known volume to find a missing dimension. Cylinders arrive in Year 9.

How do students convert between volume and capacity?

1 cm^3 = 1 mL exactly. So a 500 mL water bottle holds 500 cm^3 of water. The conversion is the same whether the container is rectangular, triangular, or any other prism shape.

How does capacity relate to litres?

1000 mL = 1 L, and 1 L = 1000 cm^3 (or 1000 cubic centimetres). So a fish tank with internal dimensions 50 cm x 30 cm x 40 cm has a volume of 60,000 cm^3 = 60 L.

Why does Year 8 work back from volume to find missing dimensions?

Real-world problems often state the volume needed (a 20 L planter box) and one or two dimensions, then ask for the third. The reverse calculation - divide volume by the other dimensions - is what shows up on tests.

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