Year 7 - Volume - Free practice

Year 7 Volume Worksheets & Practice Tests

Volume of right prisms - rectangular, triangular, and word problems.

Quick answer

How do you find the volume of a prism in Year 7?

Volume of a right prism = area of cross-section × length. For a rectangular prism use length × width × height; for a triangular prism use ½ × base × height of triangle × length. For example, a rectangular prism 5 cm × 3 cm × 4 cm has volume 60 cm³.

Generate a free maths worksheet

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

Want more than a worksheet?

Practice built from mistakes.

A worksheet on Year 7 volume is a good start. Tuterly goes further: it turns any question students get wrong into fresh practice, at the right level, on what’s likely to be in the next test or exam.

~90% of Bayside Academics students using it weekly improved their test marks

Of the Bayside Academics students who used Tuterly at least once a week, about 90% improved their school test marks.

Based on the actual school test marks of 100+ Bayside Academics students (in person and online) in Years 7 to 10, before and after using Tuterly at least once a week. How we measured this

Free worksheet Tuterly

The questionsFree worksheetThe same questions for every student on this topic.TuterlyWritten from the questions they got wrong in homework and school tests, at their level.

How manyFree worksheetOne sheet at a time.TuterlyAs many fresh questions as they need, each one different, never just the numbers swapped.*

Before a testFree worksheetPick a topic and hope it’s the right one.TuterlyA practice test covering every part of the topic. Upload the term planner and it focuses on what’s coming up.

MarkingFree worksheetCheck the answer key yourself.TuterlyMarked as they go, with the exact step that went wrong explained.

ProgressFree worksheetNothing is saved.TuterlyEvery question tracked until it’s mastered, and a weekly review for parents.

For Years 7 to 10: $8.99 a week or $29.99 a month at the launch price (from 1 April 2027, $17.99 a week or $59.99 a month), with a 7-day free trial on the monthly plan only. Better marks in 6 months, or your money back.

Or try it free now on one of their questions →

Coming soon on iPhone. Android soon after.

Free to download · 7-day free trial on monthly · Years 7 to 10 maths · On iPhone. Android coming soon

* With a subscription. Fair use applies: up to 80 snapped questions and 120 new practice questions a day per student.

Worked examples

Year 7 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 rectangular prism
Find the volume of a rectangular prism with length $12$ cm, width $5$ cm and height $4$ cm.
Show worked solution
Key idea: The volume of a rectangular prism is length times width times height.
1. Write the formula: $V = l \times w \times h$
2. Substitute the values: $V = 12 \times 5 \times 4$
3. Calculate: $V = 240$
Answer: The volume is $240$ cm³.
Example 2 · Volume of a triangular prism
A triangular prism has a triangular cross-section with a base of $6$ cm and a perpendicular height of $5$ cm. The prism has a length of $10$ cm. Find the volume of the prism.
Show worked solution
Key idea: The volume of a prism is the area of its cross-section multiplied by its length. For a triangular cross-section, use $A = \frac{1}{2} \times b \times h$ .
1. Find the area of the triangular cross-section: $A = \frac{1}{2} \times 6 \times 5 = 15$ cm²
2. Write the volume formula: $V = A \times l$
3. Substitute the values: $V = 15 \times 10$
4. Calculate: $V = 150$
Answer: The volume is $150$ cm³.
Example 3 · Volume and capacity of a garden bed
Mia is building a rectangular garden bed that is $2$ m long, $80$ cm wide and $25$ cm deep. She needs to fill it with soil. One bag of soil contains $40$ litres. How many whole bags of soil does Mia need to buy to completely fill the garden bed? (Note: $1$ litre $= 1000$ cm³)
Show worked solution
Key idea: Convert all measurements to the same unit first, then find the volume and convert to litres to compare with the bag size.
1. Convert all measurements to centimetres: length $= 200$ cm, width $= 80$ cm, height $= 25$ cm.
2. Find the volume: $V = 200 \times 80 \times 25 = 400\,000$ cm³
3. Convert to litres: $400\,000 \div 1000 = 400$ litres
4. Find the number of bags: $400 \div 40 = 10$ bags
Answer: Mia needs to buy $10$ bags of soil.

Common mistakes

Where students usually lose marks

Forgetting to halve the triangle's area

Area of triangle $= 6 \times 5 = 30$ cm², so $V = 30 \times 10 = 300$ cm³

The area of a triangle is $\frac{1}{2} \times base \times height$ , not just $base \times height$ . Always include the $\frac{1}{2}$ before multiplying by the prism's length.

Mixing up units (metres and centimetres)

$V = 2 \times 80 \times 25 = 4000$ cm³ (using 2 m without converting)

Before substituting into any formula, check that every measurement is in the same unit. Convert metres to centimetres by multiplying by $100$ , so $2$ m $= 200$ cm.

Confusing length of prism with height of triangle

Using the prism's length of $10$ cm as the height in the triangle area formula instead of $5$ cm

A triangular prism has two different heights: the perpendicular height of the triangular face, and the length the prism extends in 3D. Identify which measurement belongs to the triangle and which is the prism's length before calculating.

Forgetting to convert cm³ to litres

$V = 400\,000$ cm³, so Mia needs $400\,000 \div 40 = 10\,000$ bags

Bag sizes are given in litres, not cm³. Convert first using $1000$ cm³ $= 1$ litre, then compare with the bag size.

Try one yourself

Your turn

A triangular prism has a triangular face with base $8$ cm and perpendicular height $5$ cm. The prism is $12$ cm long. What is the volume of the prism in cm³?

Got a different volume question wrong? Upload it to Tuterly and get the worked solution and a fresh one to practise, free.

About this worksheet

Why we built it

Year 7 introduces the formula "volume = area of cross-section x length" for right prisms. These worksheets give your student varied practice on rectangular and triangular prisms, plus the wordier problems that turn up on school tests.

What's covered

Sub-skills your student will practise

✓Volume of a rectangular prism
✓Volume of a triangular prism
✓Volume in litres vs cubic centimetres
✓Compound-prism word problems (swimming pools, garden beds)
✓Working back from a known volume to find a missing dimension

From our families

Parents on the practice questions.

“Tuterly has been exactly what we needed since Tom started secondary school. Once the topic tests began, he was struggling to keep up. Now he has unlimited practice, all matched to what his class is actually covering, and his Maths results have improved noticeably.”

Rebecca M.

Year 8 · Maths

“My daughter used to leave revision until the night before. Having a platform she can dip into for fifteen minutes after dinner has completely changed that. She's calmer going into assessments, and honestly, so am I.”

Priya S.

Year 9 · Maths

“I like that I can just keep doing questions until it clicks. If I get something wrong, it shows me why, and then gives me another one like it.”

Ella, student

Year 10 · Maths

Verified parent

Frequently asked

Questions parents ask about volume

What does Year 7 volume cover?

The volume of right prisms - mostly rectangular and triangular prisms - using the formula 'area of cross-section x length'. Year 8 extends this to capacity in litres and Year 9 brings in cylinders.

What does 'right prism' mean exactly?

A right prism has its top and bottom faces parallel and the sides perpendicular to them. The cross-section (shape of the top and bottom) stays the same all the way through. Examples: rectangular boxes, triangular toblerone bars.

How do students approach a tricky volume word problem?

Identify the cross-section first, calculate its area, then multiply by the length perpendicular to that cross-section. For a swimming pool, the cross-section is usually the side view (a rectangle or trapezium).

What units does Year 7 volume use?

Cubic units - cm^3 or m^3. Capacity (mL, L) arrives in Year 8 with the relationship 1 mL = 1 cm^3. For Year 7, sticking to cubic units is enough.

Better maths marks start with the next wrong answer.

Tuterly turns every missed maths question into practice tailored towards the student, not just a generic worksheet.