Mathematics • Year 8 • Unit 3 • Lesson 12
Capacity and Mass — Mixed Challenge
Pull everything from Lesson 12 together: volume ladder (mm³–cm³–m³), capacity ladder (mL–L–kL), and the water-mass shortcut. Six mixed problems, one "find the mistake", and one open-ended design challenge.
1. Mixed problems — choose the right move
Each question pulls a different idea from Lesson 12. Decide which conversion direction applies before you start. Show your working. 3 marks each
1.1 Convert 0.5 m³ to litres.
1.2 Convert 850 mL to L.
1.3 A water bottle holds 600 mL. What is its mass (in grams) when full of water?
1.4 A rectangular bucket measures 25 cm × 25 cm × 32 cm. Find its capacity in litres.
1.5 A tank with base 50 cm × 40 cm holds exactly 20 L of water. Find its height. (Hint: convert 20 L back to cm³ first.)
1.6 A school's water tank is 2 m × 1.5 m × 1 m. Find (a) its volume in m³, (b) capacity in kL, and (c) the mass of water (in tonnes) when full.
2. Find the mistake
A Year 8 student has tried to find the mass of water in a tank measuring 50 cm × 40 cm × 30 cm. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then re-do the working correctly. 3 marks
Student's working — find mass of water in a 50 × 40 × 30 cm tank:
Line 1: V = 50 × 40 × 30 = 60,000 cm³
Line 2: 60,000 cm³ = 60,000 mL (since 1 cm³ = 1 mL)
Line 3: 60,000 mL ÷ 1000 = 60 L
Line 4: Mass = 60 g (since 1 L = 1 g for water)
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write out the corrected working in full, including the corrected final answer.
Stuck? Revisit lesson § Card 7 — the water rule is 1 L = 1 kg, not 1 g. The g rule is 1 mL = 1 g.3. Open-ended challenge — design a 10-litre tank
This question has more than one valid answer. 4 marks
3.1 A school needs a rectangular water container that holds exactly 10 litres (= 10,000 cm³). Design three different containers that work — each with whole-cm dimensions.
For each container:
(i) State the dimensions length × width × height (all in cm).
(ii) Show the check: V = l × w × h = 10,000 cm³.
(iii) State the capacity (in L) and the mass of water (in kg) when full.
Bonus: at least one of your three containers must be a cube (or near-cube) shape, and at least one must be tall and narrow (h > 2 × the largest base dimension).
How did this worksheet feel?
What I'll revisit before next class:
1.1 — 0.5 m³ to L
0.5 × 1000 = 500 L.
1.2 — 850 mL to L
850 ÷ 1000 = 0.85 L.
1.3 — 600 mL water mass
1 mL water = 1 g, so 600 mL = 600 g.
1.4 — Bucket 25 × 25 × 32
V = 25 × 25 × 32 = 20,000 cm³ = 20,000 mL = 20 L.
1.5 — Tank height from capacity
20 L = 20,000 mL = 20,000 cm³. Base area = 50 × 40 = 2000 cm². h = 20,000 ÷ 2000 = 10 cm.
1.6 — School tank
(a) V = 2 × 1.5 × 1 = 3 m³.
(b) 1 m³ = 1 kL, so 3 kL = 3000 L.
(c) 1 m³ water = 1 t, so mass = 3 t.
2 — Find the mistake
(a) The mistake is on Line 4.
(b) The student used the wrong unit: 1 L of water = 1 kg, not 1 g. (The 1 g rule applies to 1 mL.) So 60 L → 60 kg, not 60 g.
(c) Corrected working:
V = 50 × 40 × 30 = 60,000 cm³
= 60,000 mL = 60 L
Mass = 60 kg ✓ (since 1 L water = 1 kg).
Sanity check: the wrong answer (60 g) is 1000 times too small. A tank that big can't possibly hold only 60 g — that's about the mass of a chicken egg!
3 — 10 L container design (sample solutions)
There are many valid designs (l × w × h = 10,000 cm³). Three good examples:
Design 1 — long and shallow: 50 cm × 20 cm × 10 cm.
Check: 50 × 20 × 10 = 10,000 ✓. Capacity = 10 L; mass = 10 kg of water.
Design 2 — near-cube: 22 cm × 22 cm × 20.7 cm.
Check: 22 × 22 × 20.7 ≈ 10,019 cm³ (within 0.2% of 10 L). Capacity ≈ 10 L; mass ≈ 10 kg.
(Or whole-cm near-cube: 20 × 20 × 25 = 10,000 ✓.)
Design 3 — tall and narrow: 10 cm × 10 cm × 100 cm.
Check: 10 × 10 × 100 = 10,000 ✓. Height 100 cm > 2 × 10 cm. Capacity = 10 L; mass = 10 kg.
Other valid answers: 25 × 20 × 20 = 10,000 ✓; 40 × 25 × 10 = 10,000 ✓; 50 × 10 × 20 = 10,000 ✓; 100 × 10 × 10 = 10,000 ✓.
Marking: 1 mark per valid design with correct check (volume = 10,000 cm³ ± 1%) up to 3 marks. 1 bonus mark for satisfying both shape constraints (one near-cube AND one tall-and-narrow).