Volume and surface area: designing a water tank
Shape a cuboid water tank, count the litres it holds, open it into its net and find the tank that needs the least metal.
Core concept
In short: Fill a box-shaped tank with cubes and wrap it to find its volume and surface.
Volume = length × width × height counts the unit cubes inside; surface area adds up the six faces of the net
Topic: Solids: volume and surface area
A family orders a closed metal water tank shaped like a cuboid, measured in decimetres (dm). The volume: How much space something takes up, measured in millilitres or cubic centimetres. All key words is how many 1 dm cubes fit inside: length × width × height, in dm³. One cubic decimetre holds exactly 1 litre, so the volume in dm³ is the capacity in litres. The metal needed is the surface area: How much flat space a shape covers, measured in square units like cm². All key words: opened out flat, the tank is a net of six rectangles in three matching pairs, so the surface area is 2(lw + lh + wh) dm². Tanks can hold the same amount of water but need different amounts of metal.
What you will learn
- Find the volume of a cuboid by counting unit cubes and with l × w × h.
- Draw the net of a cuboid and find its surface area.
- Compare cuboids with the same volume and different surface areas.
Before you start
- Area of a rectangle and multiplication.
Materials
- Card, scissors and tape to build a box from a net
Equipment
- A ruler and a 1 litre bottle
Procedure
- Drag the right side of the tank to change its length and the top to change its height; tap − or + for its width.
- Tap the chip to open the tank out into its net, and again to fold it back.
- Make a cube-shaped tank, and record the tank opened out as a net.
- Make a 24 litre tank, then find the 24 litre tank that needs the least metal.
How this simulation is simplified
- The tank is closed, and the metal's thickness is ignored. 1 dm³ = 1 litre.