Mathematics • Year 8 • Unit 3 • Lesson 12
Capacity and Mass
Build fluency with the conversion chain: 1 cm³ = 1 mL = 1 g (water), and the ×1000 jumps between mL/L/kL and g/kg/t. One worked example, one guided, then eight independent conversions.
1. I do — fully worked example
Read every line. Each step has a short reason so you see why the conversion goes in that direction.
Problem. A rectangular tank measures 40 cm × 30 cm × 25 cm. Find its capacity in litres, and the mass of water it holds (in kg).
Step 1 — Find the volume.
V = 40 × 30 × 25 = 30,000 cm³
Reason: volume of a rectangular prism = length × width × height. Units cm × cm × cm = cm³.
Step 2 — Convert cm³ to mL.
30,000 cm³ = 30,000 mL
Reason: 1 cm³ = 1 mL exactly. No arithmetic needed.
Step 3 — Convert mL to L.
30,000 mL ÷ 1000 = 30 L
Reason: 1 L = 1000 mL, so going to the larger unit (L) means dividing.
Step 4 — Convert L to kg (water).
30 L of water → mass = 30 kg
Reason: for water only, 1 L = 1 kg exactly. Mass and capacity numbers match.
Answer: capacity = 30 L; mass of water = 30 kg.
2. We do — fill in the missing steps
Same shape as Section 1, with the working faded. Fill in each blank. 4 marks
Problem. A box measures 20 × 10 × 15 cm. Find its capacity in litres and the mass of water it holds (in kg).
Step 1 — Find the volume:
V = 20 × 10 × 15 = ______ cm³
Step 2 — Convert cm³ to mL (1 cm³ = ______ mL):
______ cm³ = ______ mL
Step 3 — Convert mL to L (divide by ______):
______ mL ÷ 1000 = ______ L
Step 4 — Mass of water (1 L = ______ kg):
Mass = ______ kg
3. You do — independent practice
Show every conversion step and write units. The first four are foundation (single-step). The middle two are standard (two-step). The last two are extension (full chain, including m³).
Foundation — single-step conversions
3.1 Convert 5000 mL to L. 1 mark
3.2 Convert 3 L to mL. 1 mark
3.3 Find the mass of 8 L of water in kg. 1 mark
3.4 Find the mass of 250 mL of water in g. 1 mark
Standard — two-step conversions
3.5 Convert 4500 cm³ to L. (Hint: cm³ → mL → L.) 2 marks
3.6 Find the mass of 2500 mL of water in kg. (Hint: mL → g → kg.) 2 marks
Extension — full chain including m³
3.7 Convert 3.5 m³ to cm³, then to L. (Hint: 1 m³ = 10⁶ cm³.) 2 marks
3.8 A swimming pool holds 6 m³ of water. Find (a) the capacity in litres and (b) the mass of the water in tonnes. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (20 × 10 × 15)
Step 1: V = 20 × 10 × 15 = 3000 cm³.
Step 2: 1 cm³ = 1 mL, so 3000 cm³ = 3000 mL.
Step 3: divide by 1000, so 3000 mL ÷ 1000 = 3 L.
Step 4: 1 L = 1 kg, so mass = 3 kg.
3.1 — 5000 mL to L
5000 ÷ 1000 = 5 L.
3.2 — 3 L to mL
3 × 1000 = 3000 mL.
3.3 — Mass of 8 L of water
1 L water = 1 kg, so 8 L = 8 kg.
3.4 — Mass of 250 mL of water
1 mL water = 1 g, so 250 mL = 250 g.
3.5 — 4500 cm³ to L
4500 cm³ = 4500 mL (1:1) = 4500 ÷ 1000 = 4.5 L.
3.6 — Mass of 2500 mL water
2500 mL water = 2500 g, then 2500 ÷ 1000 = 2.5 kg.
3.7 — 3.5 m³ to cm³ to L
3.5 × 10⁶ = 3,500,000 cm³. Then 3,500,000 cm³ = 3,500,000 mL = 3,500,000 ÷ 1000 = 3500 L. (Or directly: 3.5 m³ × 1000 = 3500 L.)
3.8 — 6 m³ of water
(a) 6 × 1000 = 6000 L.
(b) 6000 L water = 6000 kg = 6000 ÷ 1000 = 6 t (using 1 m³ water = 1 t).