Week 29 · Volume of a cuboid and how doubling the sides changes it · 3 lessons
2
Volume stories: boxes, tanks and how many fit
Discover Mathematics P6: Term 2, Unit 13, Lessons 3–4
GoalSolve volume stories: how many boxes fit in a carton and how much a tank holds.
New words
fit · how many small things go inside a bigger onetank · a container that holds water or other liquidcapacity · how much a container can hold; 1 L = 1,000 cm³
Explanation
Volume stories ask two kinds of question. The first: how much space is there? Multiply the three sides. The second: how many small boxes fit in a big one? You can divide the volumes, or count along each side. If a carton is 60 cm × 40 cm × 30 cm and a box is 20 cm × 10 cm × 10 cm, then 60 ÷ 20 = 3 boxes along the length, 40 ÷ 10 = 4 across and 30 ÷ 10 = 3 up: 3 × 4 × 3 = 36 boxes. Dividing the volumes gives the same: 72,000 ÷ 2,000 = 36. Counting along the sides is safer when the sizes do not fit exactly. A useful fact: a container of volume 1,000 cm³ holds 1 litre, and 1 m³ holds 1,000 litres.
★Remember
How many fit? Divide the length, the width and the height of the big box by those of the small box, then multiply the three answers.
Worked examples
Carton
Box
How many along
Length
60 cm
20 cm
3
Width
40 cm
10 cm
4
Height
30 cm
10 cm
3
A carton is 60 cm by 40 cm by 30 cm. Its volume is 60 × 40 × 30 = 72,000 cm³. A box is 20 cm by 10 cm by 10 cm, with volume 2,000 cm³. 72,000 ÷ 2,000 = 36 boxes. Along the sides: 3 × 4 × 3 = 36.
A water tank is 2 m long, 1.5 m wide and 1 m high. Volume = 2 × 1.5 × 1 = 3 m³. Since 1 m³ holds 1,000 litres, the tank holds 3,000 litres.
A fish tank is 40 cm by 25 cm by 20 cm. Volume = 40 × 25 × 20 = 20,000 cm³. Since 1,000 cm³ is 1 litre, it holds 20 litres.
Class activity
How many fit? Find a small box (matchbox or tea box) and a bigger box. Measure both and work out how many small boxes fit in the big one. Try to pack them and check.
Practice
1
A classroom is 8 m long, 6 m wide and 3 m high. Find its volume.
8 × 6 × 3 = 144 m³.
2
How many boxes 2 cm by 2 cm by 2 cm fit in a box 12 cm by 10 cm by 6 cm?
