Discover Mathematics P5: Term 2, Unit 11, Lessons 7–9
GoalSolve real-life volume problems with cm³, m³ and litres, including packing and filling.
New words
pack · to fit smaller things into a bigger containercapacity · the volume of liquid a container can holdper · for each one, such as 150 LE per cubic metre
Explanation
Volume stories use the same steps. Read the story and draw the container. Choose the formula V = l × w × h. Check that all the measures use the same unit. Calculate. Then answer the question in the right unit. To find how many small boxes fit inside a big box, you can divide the volumes, or count how many fit along each edge and multiply. A crate 60 cm × 40 cm × 30 cm holds 6 × 4 × 3 = 72 cubes of side 10 cm. To change cm³ into litres, divide by 1,000. When money is involved, multiply the volume by the price per unit.
Draw→Formula→Same units→Calculate→Answer
Worked examples
A crate is 60 cm long, 40 cm wide and 30 cm high. How many cubes of side 10 cm fit? Along the length 60 ÷ 10 = 6, along the width 40 ÷ 10 = 4, along the height 30 ÷ 10 = 3. So 6 × 4 × 3 = 72 cubes. Check with volumes: 60 × 40 × 30 = 72,000 and 72,000 ÷ 1,000 = 72.
A tank is 50 cm × 40 cm × 30 cm. V = 50 × 40 × 30 = 60,000 cm³ = 60 litres. If a bucket holds 5 litres, the tank needs 60 ÷ 5 = 12 buckets to fill it.
A lorry carries sand in a space 3 m long, 2 m wide and 1 m high. V = 3 × 2 × 1 = 6 m³. Sand costs 150 LE per cubic metre, so a full load costs 6 × 150 = 900 LE.
Class activity
Pack the box. Find a shoebox and some small boxes or blocks of the same size (for example matchboxes or sugar cubes). Estimate how many small boxes fit in the shoebox. Then measure everything, calculate how many should fit by counting along each edge, and pack to check.
Practice
1
A pool is 10 m long and 5 m wide. How many cubic metres of water are in it when it is 1 m deep, and how many more are needed to make it 2 m deep?
At 1 m: 10 × 5 × 1 = 50 m³. At 2 m: 10 × 5 × 2 = 100 m³. More needed: 100 − 50 = 50 m³.
2
How many cubes of side 5 cm fit in a box 20 cm × 10 cm × 10 cm?
A juice carton is 10 cm × 5 cm × 20 cm. How many cartons fit in a crate 40 cm × 30 cm × 20 cm if they stand with their 10 cm side along the length and 5 cm side along the width?
Along the length 40 ÷ 10 = 4. Along the width 30 ÷ 5 = 6. The height 20 cm fits one carton. 4 × 6 × 1 = 24 cartons. Check: 40 × 30 × 20 = 24,000 and each carton is 1,000 cm³: 24.
