Mathematics • Year 8 • Unit 3 • Lesson 10
Volume in the Real World
Use V = A_base × h to solve real problems: filling pools, designing aquariums, packing trucks, and rationing water tanks. Then explain when volume matters more than surface area.
1. Word problems
Each problem hides a prism. Sketch the shape, identify the cross-section, pick V = A_base × h, then convert units if needed. Show all working.
1.1 — Filling a fish tank. An aquarium is a rectangular prism 80 cm long, 40 cm wide, and 50 cm tall. The owner fills it to ¾ full.
(a) Find the full volume of the tank in cm³.
(b) Find ¾ of that volume in litres (1000 cm³ = 1 L).
(c) The household tap delivers 8 L/minute. How many minutes to fill the tank to ¾? 3 marks
1.2 — Packing the moving truck. A removalist's truck cargo area is a rectangular prism 4.5 m long, 2.2 m wide, and 2 m tall. The customer's boxes are all rectangular prisms 50 cm × 40 cm × 30 cm (= 0.5 m × 0.4 m × 0.3 m).
(a) Find the truck's cargo volume in m³.
(b) Find the volume of one box in m³.
(c) Assuming perfect packing (no gaps), what's the maximum number of boxes the truck can hold? 3 marks
1.3 — Water tank rationing. A rectangular rainwater tank is 2 m long, 1 m wide, and 1.5 m tall. A family uses 250 L of water per day.
(a) Find the tank's full capacity in m³ and in L.
(b) If the tank starts full and no rain falls, how many full days will the water last? 3 marks
1.4 — Tent (triangular prism). A camping tent is a triangular prism. The triangular cross-section has base 2 m and height 1.5 m (the floor and peak height). The tent length is 3 m.
(a) Find the cross-section area of the triangle.
(b) Find the total internal volume of the tent.
(c) If the campers each need 0.5 m³ of breathing space, how many people can sleep comfortably? 3 marks
1.5 — Concrete steps (L-shape). A set of concrete steps has a cross-section that is L-shaped: a 30 cm × 60 cm vertical rectangle joined to a 60 cm × 30 cm horizontal rectangle (the step). The steps are 1.2 m wide.
(a) Find the L-shape area (in cm²).
(b) Find the volume of concrete needed in m³. (Hint: convert lengths to metres first OR keep in cm and convert at the end. 1 m³ = 1 000 000 cm³.) 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 to find the capacity of a fish tank in litres. The tank is 60 cm × 30 cm × 40 cm. They write "V = 60 × 30 × 40 = 72 000 cm³, so capacity = 72 000 L". In your own words, explain (i) what mistake they have made, (ii) what the correct capacity in litres is and how to get it, and (iii) why a Year 8 student should always check whether their answer is sensible for a household object. Use the phrase "1000 cm³ = 1 L" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Fish tank 80 × 40 × 50
(a) V_full = 80 × 40 × 50 = 160 000 cm³.
(b) Full = 160 L; ¾ full = ¾ × 160 = 120 L.
(c) 120 ÷ 8 = 15 minutes.
1.2 — Moving truck
(a) Truck V = 4.5 × 2.2 × 2 = 19.8 m³.
(b) Box V = 0.5 × 0.4 × 0.3 = 0.06 m³.
(c) Boxes = 19.8 / 0.06 = 330 boxes (maximum, perfect packing).
1.3 — Rainwater tank 2 × 1 × 1.5
(a) V = 3 m³ = 3000 L.
(b) Days = 3000 / 250 = 12 days.
1.4 — Tent (triangular prism)
(a) A_triangle = ½ × 2 × 1.5 = 1.5 m².
(b) V = 1.5 × 3 = 4.5 m³.
(c) People = 4.5 / 0.5 = 9 people.
1.5 — Concrete L-shape steps
(a) A_L = (30 × 60) + (60 × 30) = 1800 + 1800 = 3600 cm².
(b) Width = 1.2 m = 120 cm. V = 3600 × 120 = 432 000 cm³ = 0.432 m³.
2.1 — Explain your thinking (sample response)
The classmate has correctly calculated the volume as 72 000 cm³, but then they assumed cm³ converts directly to L. They have forgotten that 1000 cm³ = 1 L (not 1 cm³ = 1 L). The correct capacity is 72 000 ÷ 1000 = 72 L. A Year 8 student should sanity-check their answer: 72 000 L is the size of a small swimming pool, not a household fish tank! A typical home aquarium holds maybe 50–100 L, so 72 L is exactly right.
Marking: 1 mark for spotting "treated cm³ as L"; 1 mark for correct conversion using "1000 cm³ = 1 L"; 1 mark for the correct final answer of 72 L; 1 mark for the sensible sanity check.