The idea, step by step
Volume counts space inside
A prism has the same cross-section all the way along its length. Here we use right prisms, so the prism length is the perpendicular distance between the matching ends. First find the area of one end. Multiplying that area by this length counts the layers of space. A cuboid is a rectangular prism, so its formula is length × width × height. Write volume in cubic units.
Triangular prisms use triangle area first
If the end is a triangle, find half the triangle base times its perpendicular height. Then multiply by the distance between the two triangular ends. This prism length is a different measurement from the triangle height. Read the diagram carefully.
A volume of 1 cm³ holds 1 mL. This lets you connect the space inside a container to its capacity, but only if the dimensions describe the inside and no extra space is lost to walls.
A common trap
Multiplying the three dimensions of a triangular prism without halving.
Instead: The cross-section is a triangle, not a rectangle. Find ½ × base × perpendicular height before multiplying by prism length.
See the thinking
Rectangular prism
Find the volume of a cuboid 8 cm long, 3 cm deep and 4 cm high.
- Area of rectangular end = 3 × 4 = 12 cm².
- Multiply by length: 12 × 8 = 96 cm³.
Triangular prism
A triangular prism has end base 6 cm, perpendicular end height 4 cm and length 10 cm. Find its volume.
- Triangle area = ½ × 6 × 4 = 12 cm².
- Prism volume = 12 × 10 = 120 cm³.
Check your understanding
A prism has cross-section area 15 cm² and length 8 cm. Find its volume.
Show answer
120 cm³
15 × 8 = 120; cm² × cm gives cm³.
Your turn
6 questions · 14 marks · Work at your own pace.
Read the questions online
- Find the volume of a cuboid 5 cm by 4 cm by 3 cm.2 marks
- A prism has cross-section area 18 m² and length 7 m. Find its volume.1 mark
- Find the volume of a triangular prism with end base 8 cm, perpendicular end height 3 cm and prism length 12 cm.3 marks
- A cuboid has volume 240 cm³. Its base is 8 cm by 5 cm. Find its height.3 marks
- The inside of a rectangular container is 10 cm by 8 cm by 5 cm. How many mL can it hold?2 marks
- Two prisms have the same cross-section area. One is 6 cm long and the other is 15 cm long. The shorter has volume 48 cm³. Find the longer volume.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find the volume of a cuboid 5 cm by 4 cm by 3 cm.2 marks
5 × 4 × 3 = 60 cm³.
60 cm³ - A prism has cross-section area 18 m² and length 7 m. Find its volume.1 mark
18 × 7 = 126 m³.
126 m³ - Find the volume of a triangular prism with end base 8 cm, perpendicular end height 3 cm and prism length 12 cm.3 marks
End area = ½ × 8 × 3 = 12 cm².
Volume = 12 × 12 = 144 cm³.
144 cm³ - A cuboid has volume 240 cm³. Its base is 8 cm by 5 cm. Find its height.3 marks
Base area = 8 × 5 = 40 cm².
Height = volume ÷ base area.
240 ÷ 40 = 6 cm.
6 cm - The inside of a rectangular container is 10 cm by 8 cm by 5 cm. How many mL can it hold?2 marks
Volume = 10 × 8 × 5 = 400 cm³.
1 cm³ = 1 mL.
400 mL - Two prisms have the same cross-section area. One is 6 cm long and the other is 15 cm long. The shorter has volume 48 cm³. Find the longer volume.3 marks
Cross-section area = 48 ÷ 6 = 8 cm².
Longer volume = 8 × 15 = 120 cm³.
120 cm³
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 7 measurement and spatial representation: areas of triangles/parallelograms, prism volumes, circle circumference, nets and views. Precision is integrated into practical measurement; circle area is not introduced here.
Official curriculum source ↗