Cuboid volume
FoundationVolume = length × width × height.
After this lesson, you can:
- Cuboid volume = length × width × height
- Cube volume = edge × edge × edge
- Volume units are cubic units (cm³, m³)
1Summary 重點摘要
Volume = length × width × height.
2Vocabulary cards Vocabulary
V
Volume體積
How much space a solid takes, e.g. how many 1 cm³ cubes fill a box.
L
Length長
The longest edge of the cuboid, e.g. 5 cm.
W
Width闊
The sideways edge of the cuboid, e.g. 3 cm.
H
Height高
The vertical edge of the cuboid, e.g. 2 cm.
C
Cubic units立方單位
Volume units, e.g. cm³, m³.
C
Cuboid長方體
A solid with six rectangular faces, like a tissue box.
C
Cube正方體
A solid with six square faces, like a die; volume = edge × edge × edge.
L
Layer分層
Think of volume in layers: fill the base, then stack up.
3Step by step Steps
- Step 1: The formulaA cuboid's volume is V = length × width × height, for example 2 × 3 × 4. Measure all three edges in the same unit, along each edge to the opposite face.
- Step 2: Think in layersUse 1-cm cubes to picture it: the base layer holds 2 × 3 = 6 cubes, which is the base area, and stacking 4 layers gives 6 × 4 = 24 cubes, so the volume is 24 cm³. The formula is really the base area times the height.
- Step 3: Substitute and calculateFirst 2 × 3 = 6, then 6 × 4 = 24, so V = 24. Multiplying in order, base area first and height last, keeps the working clear and makes mistakes unlikely.
- Step 4: The cube special caseA cube has three equal edges, so its formula is edge × edge × edge. A cube of edge 3 cm has volume 3 × 3 × 3 = 27 cm³. A cube is just a cuboid whose length, width and height are all equal.
- Step 5: Use the right unitsVolume takes cubic units: edges measured in centimetres give a volume in cubic centimetres, written cm³. The units cm² (area) and cm (length) are different measures and must not be mixed. Always end a volume answer with a cubic unit.
- Step 6: Find a missing edgeKnowing the volume and two edges gives the third: volume 24 with length 2 and width 3 has height 24 ÷ (2 × 3) = 24 ÷ 6 = 4 cm. Dividing the volume by the product of the two known edges undoes the formula.
4Diagrams Diagrams
5Worked example Example
Example: a box is 5 cm long, 4 cm wide and 3 cm high. What is its volume?
- Write the formula: volume of a cuboid V = length × width × height.
- Substitute: V = 5 × 4 × 3.
- First work out 5 × 4 = 20, which is the area of the base.
- Then 20 × 3 = 60, the base area times the height.
- Attach cubic units: the box's volume is 60 cm³.
- Answer: The box's volume is 60 cm³. We first found the base area 5 × 4 = 20, then multiplied by the height 3 to get 60, and attached the cubic unit cm³. Picture it as layers of 20 one-cm cubes stacked 3 high, 60 cubes in all, which agrees with the formula.
6Common mistakes Mistakes
✗ Multiplying only two edges as if it were area: 5 × 4 = 20.
✓ Volume needs all three: 5 × 4 × 3 = 60 cm³.
✗ Writing volume units as cm².
✓ Volume uses cubic units cm³; cm² is area.
✗ Mixing up volume with surface area.
✓ Volume measures space (cm³); surface area measures wrapping (cm²) — different things.
✗ Using addition to find a missing edge.
✓ Use division: height = 24 ÷ (2 × 3) = 4 cm.
7Quick check Quick check
Q1A cuboid 2 × 3 × 4 cm. Volume?
Answer: 2 × 3 × 4 = 24 cm³.
Did you get it right?
Q2A cube with edge 4 cm. Volume?
Answer: 4 × 4 × 4 = 64 cm³.
Did you get it right?
Q3Volume 36 cm³, length 3 cm, width 4 cm. Height?
Answer: 36 ÷ (3 × 4) = 36 ÷ 12 = 3 cm.
Did you get it right?
Q4Should volume units be cm, cm² or cm³?
Answer: cm³ (cubic centimetres).
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Q5A cube box 10 × 10 × 10 cm. What is the volume in cm³?
Answer: 10 × 10 × 10 = 1000 cm³ (exactly 1 litre).
Did you get it right?
8Recap Recap
- Cuboid volume = length × width × height
- Cube volume = edge × edge × edge
- Volume units are cubic units (cm³, m³)
- Volume measures space; surface area measures the outer skin
- With volume and two edges, divide to find the third