A net is a two-dimensional pattern that can be folded to make a three-dimensional solid. Every face of the solid appears once in its net. Cutting a solid open along its edges and laying it flat produces one of its possible nets.
Nets of prisms and pyramids
The net of a solid is made of the same number of pieces as its faces. A cuboid has 6 rectangles; a cube has 6 identical squares; a triangular prism has 2 triangles and 3 rectangles (5 pieces); a square pyramid has 1 square and 4 triangles (5 pieces).
Worked example
Find the number of pieces in the net of a pentagonal prism. A prism has n + 2 faces, so with n = 5 it has 7 faces: 2 pentagons and 5 rectangles. Its net has 7 pieces.
Nets of curved solids
The net of a cylinder is 2 circles (top and bottom) plus 1 rectangle that curls round. The width of that rectangle equals the circumference of the circle, 2πr. The net of a cone is 1 circle (the base) plus 1 sector (the curved surface).
Key idea
For a cylinder, the rectangle in the net has length = circumference = 2πr = πd. If r = 7 cm and π = 22/7, the length is 2 × 22/7 × 7 = 44 cm.
Remember
- Number of pieces in a net = number of faces of the solid.
- A cylinder's net = 2 circles + 1 rectangle.
- A cone's net = 1 circle + 1 sector; a sphere has no flat net.