Volume and surface area of a box
Change the length, breadth and height of a cardboard box. Find how much it holds (volume) and how much cardboard it needs (surface area), and see that boxes with the same volume can need different amounts of cardboard.
Core concept
The volume of a cuboid is length × breadth × height and its total surface area is 2(lb + bh + hl); a cube is a cuboid with all edges equal
Topic: Perimeter, area and volume
A cuboid, like a matchbox or a brick, has 6 rectangular faces in 3 matching pairs. Its volume: How much space something takes up, measured in millilitres or cubic centimetres. All key words, the space inside, is length × breadth × height, measured in cubic centimetres (cm³). Its total surface area: How much flat space a shape covers, measured in square units like cm². All key words, the cardboard needed to make it, is the area of all 6 faces: 2(lb + bh + hl) square centimetres (cm²). A cube has every edge the same, a, so its volume is a³ and its surface area is 6a². Box makers care about both: the volume says how much fits inside, and the surface area says how much material it costs.
What you will learn
- Calculate the volume of a cuboid and a cube.
- Calculate the total surface area of a cuboid and a cube.
- Explain the difference between volume and surface area and their units.
Before you start
- Know how to find the area of a rectangle.
Materials
- An empty matchbox or carton, scissors, a ruler
Equipment
- Centimetre cubes
Procedure
- Record a box 5 cm × 4 cm × 3 cm.
- Make it a 4 cm cube and record.
- Double the length of the first box and record.
- Record a box 6 cm × 5 cm × 2 cm.
How this simulation is simplified
- The cardboard has no thickness and no flaps.