Boxes and Sketches

A net is a flat shape that folds into a 3D shape. Net of a cube: 6 squares connected. Net of a cuboid: 6 rectangles (opposite faces equal). Net of a cylinder: 2 circles + 1 rectangle. Net of a cone: 1 circle + 1 sector. Making a net: draw a box (cuboid), cut along edges, unfold flat — that's the net! Nets are used in packaging design — manufacturers design box shapes (nets) for most efficient use of cardboard.

Volume = amount of space a 3D shape occupies. Unit: cubic centimetres (cm³) or cubic metres (m³). Volume of a cuboid: length × breadth × height. Example: box 5 cm × 3 cm × 4 cm = 60 cm³. Volume of a cube: side³. 4 cm cube = 4³ = 64 cm³. A litre = 1000 cm³. How many 1 cm cubes fill a 5×4×3 box? 60 cubes! Volume = number of unit cubes that fill a shape.

Surface area = total area of all faces of a 3D shape. Cuboid: SA = 2(lb + bh + lh). Example: 5×3×4 cm cuboid: 2(5×3 + 3×4 + 5×4) = 2(15+12+20) = 2×47 = 94 cm². Cube: SA = 6×side². 4 cm cube: 6×16 = 96 cm². Surface area determines how much paint/wrapping needed. Volume determines how much it holds. Both are important in packaging!