Mathematics • Year 8 • Unit 3 • Lesson 12
Capacity and Mass in the Real World
Use 1 cm³ = 1 mL = 1 g (water) where it actually shows up: backyard pools, water bills, fish tanks, milk jugs and tipper trucks. Then explain your thinking in your own words.
1. Word problems
Each problem chains volume → capacity → mass. Always find volume first, then convert step by step. Write units at every line — single answers without working earn only half marks.
1.1 — Backyard pool. A rectangular pool is 5 m long, 2.5 m wide and 1.2 m deep.
(a) Find its volume in m³.
(b) Convert to litres (1 m³ = 1000 L).
(c) If a council tanker delivers water at 4000 L/min, how long (in minutes) does it take to fill the pool? 3 marks
1.2 — Pool water mass. Using the pool from question 1.1 (15 m³):
(a) Find the mass of all the water in kg (1 L water = 1 kg).
(b) Convert to tonnes (1 t = 1000 kg).
(c) The hook in the lesson said "a 250,000 L pool weighs 250 t." Check: does your answer for (b) match the rule 1 m³ water = 1 t? 3 marks
1.3 — Fish tank. A rectangular fish tank measures 60 cm × 30 cm × 40 cm and is filled to the top with water.
(a) Find its volume in cm³.
(b) Convert to litres.
(c) Find the mass of the water in kg. (Will a single person be able to lift the full tank?) 3 marks
1.4 — Milk jug. A milk jug holds 3 litres.
(a) Convert 3 L to mL.
(b) Convert 3 L to cm³.
(c) If milk has the same density as water (close enough), find the mass of the milk in g and in kg. 3 marks
1.5 — Tipper truck of water. A tipper truck's water tank is a rectangular prism 4 m × 2 m × 1.5 m.
(a) Find the tank volume in m³.
(b) Convert to litres and to kilolitres.
(c) Find the mass of the water in tonnes. (Why does this matter for road safety / bridge load limits?) 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate is asked: "Convert 1 m³ to L." They write "1 m³ = 100 L because 1 m = 100 cm." In your own words, explain (i) what mistake they have made, (ii) what the correct answer is and how to get it, and (iii) why the linear conversion (×100) is not the same as the volume conversion. Use the phrase "cube the conversion factor" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Backyard pool
(a) V = 5 × 2.5 × 1.2 = 15 m³.
(b) 15 × 1000 = 15,000 L.
(c) 15,000 ÷ 4000 = 3.75 minutes (= 3 min 45 s).
1.2 — Pool mass
(a) 15,000 L water = 15,000 kg.
(b) 15,000 ÷ 1000 = 15 t.
(c) Yes, 15 m³ × 1 t/m³ = 15 t ✓ — the rule matches.
1.3 — Fish tank
(a) V = 60 × 30 × 40 = 72,000 cm³.
(b) 72,000 cm³ = 72,000 mL ÷ 1000 = 72 L.
(c) 72 kg — far too heavy for one person to lift safely. Empty the tank before moving it!
1.4 — Milk jug
(a) 3 L × 1000 = 3000 mL.
(b) 3 L = 3000 cm³ (since 1 mL = 1 cm³).
(c) Mass ≈ 3000 g = 3 kg (using the water rule).
1.5 — Tipper truck water
(a) V = 4 × 2 × 1.5 = 12 m³.
(b) 12 × 1000 = 12,000 L = 12 kL.
(c) 12 t. This matters because every bridge has a "max load" sign. A 12 t water load + the truck's own mass can exceed limits, so drivers must plan their route accordingly.
2.1 — Explain your thinking (sample response)
The classmate has confused the linear conversion (1 m = 100 cm) with the volume conversion. To go from m³ to cm³, you must cube the conversion factor: 1 m³ = (100 cm)³ = 100 × 100 × 100 = 1,000,000 cm³. Then 1,000,000 cm³ = 1,000,000 mL = 1,000,000 ÷ 1000 = 1000 L. So 1 m³ = 1000 L, not 100 L. The reason for the cube is that volume measures 3 dimensions (length × width × height), so when each linear measurement is scaled up by 100, the volume scales up by 100 × 100 × 100. Their answer of 100 L is exactly 10,000 times too small.
Marking: 1 mark for identifying "used linear factor instead of cube"; 1 mark for showing 1 m³ = 10⁶ cm³ = 1000 L; 1 mark for the "3 dimensions" reasoning; 1 mark for using the phrase "cube the conversion factor" in a clear sentence.