Lesson 17: Volume Calculations
BasicCuboid volume = length × width × height. Unit is cm³ or m³. Learn to calculate cuboid, cube volume and unit conversion.
After this lesson, you can:
- Cuboid volume = length × width × height
- Cube volume = side³
- 1 L = 1000 cm³
文體小知識：體積 = 長 × 闊 × 高
Before this lesson you should know: Lesson 16: Introduction to 3D Shapes
§Text Passage
1Volume: how much space a 3D shape takes. Cuboid volume formula: V = length × width × height. For example, 5 × 3 × 2 = 30 cm³.
2Cube volume: all sides equal, so V = side × side × side = side³. For example, side 4 cm, volume = 4³ = 64 cm³.
3Volume units: cm³, m³, mL, L. 1 L = 1000 mL = 1000 cm³. 1 m³ = 1000 L.
1Summary 重點摘要
Cuboid volume = length × width × height. Unit is cm³ or m³. Learn to calculate cuboid, cube volume and unit conversion.
2Vocabulary cards Vocabulary
v
volume名詞
Space taken up
c
cubic centimetre名詞
cm³
c
cubic metre名詞
m³
l
litre名詞
Litre, L
m
millilitre名詞
Millilitre, mL
c
capacity名詞
How much it can hold
l
length名詞
How long
w
width名詞
How wide
h
height名詞
How tall
3Step by step Steps
- Block 1: Cuboid Volume FormulaThe cuboid volume formula is V = length × width × height. Example: a cuboid 10 cm long, 5 cm wide and 4 cm high has volume 10 × 5 × 4 = 200 cm³. Picture stacking layers on the base: base area 50 cm², each layer 1 cm tall, four layers make 200 cm³.
- Block 2: Cube VolumeA cube is a cuboid with equal length, width and height, so V = side × side × side, the cube of the side. Example: a cube of side 6 cm has volume 6 × 6 × 6 = 216 cm³. Work in two steps, 6 × 6 = 36 and then 36 × 6, to avoid mistakes.
- Block 3: Unit ConversionVolume units step up by 1000 in three directions: 1 m³ = 100 cm × 100 cm × 100 cm = 1,000,000 cm³, one million cubic centimetres. Because length, width and height each get converted, 100 × 100 × 100 = 1,000,000. Changing m³ to cm³ means multiplying by 1,000,000, not 100.
- Block 4: Capacity UnitsCapacity is fixed to volume: 1 L = 1000 cm³ and 1 mL = 1 cm³. Example: a tank 10 cm long, 10 cm wide and 10 cm high has volume 1000 cm³, exactly 1 L. For 'how much water' questions, find the volume in cm³ first, then divide by 1000 to change it into litres.
- Block 5: Known Volume, Find HeightWith the volume and the base known, divide to find the height: height = volume ÷ (length × width). Example: volume 200 cm³ with length 10 cm and width 5 cm gives height = 200 ÷ 50 = 4 cm. This runs the multiplication formula backwards: find the base area first, then divide the volume by it.
- Block 6: Word Problem: Water TankExample: a tank is 50 cm long, 40 cm wide and 30 cm high; how many litres fill it? Volume = 50 × 40 × 30 = 60,000 cm³, then convert: 60,000 ÷ 1000 = 60 L. Answer in two stages — find the volume, convert the unit, then state 'the tank holds 60 litres of water'.
4Diagrams Diagrams
5Worked example Example
Example: A cuboid is 8 cm long, 5 cm wide and 3 cm high. What is its volume?
- Step 1: write the cuboid volume formula V = length × width × height, matching the numbers 8, 5 and 3.
- Step 2: find the base area first: length × width = 8 × 5 = 40 cm².
- Step 3: multiply the base area by the height, V = 40 × 3 = 120 cm³.
- Step 4: check units and reasonableness — all three lengths are in cm, so the unit is cm³; 120 cm³ is about half a cup, which is sensible.
- Answer: Answer: the volume of the cuboid is 120 cm³. Finding the base area first and then multiplying by the height gives the same result as multiplying all three numbers at once, but the step-by-step way is clearer. Volume units come from multiplying three lengths, hence cm³; if capacity is asked, remember 1000 cm³ = 1 L.
6Common mistakes Mistakes
✗ Area: cm³
✓ Area: cm²; volume: cm³
✗ Cube: don't use side³
✓ Cube volume = side × side × side
✗ 1 m³ = 1000 cm³
✓ 1 m³ = 1,000,000 cm³
✗ Forget to multiply height
✓ Volume: multiply length, width, height
7Quick check Quick check
Q110 × 4 × 2 cm. Volume?
Answer: 80 cm³
Did you get it right?
Q2Cube side 5 cm. Volume?
Answer: 125 cm³
Did you get it right?
Q31 L = ? cm³
Answer: 1000 cm³
Did you get it right?
Q41 m³ = ? L
Answer: 1000 L
Did you get it right?
Q5Volume formula?
Answer: Length × width × height
Did you get it right?
8Recap Recap
- Cuboid volume = length × width × height
- Cube volume = side³
- 1 L = 1000 cm³
- 1 m³ = 1000 L
- Volume unit: cm³ / m³