Solid shapes · Usually met around P5
Nets
No 2 × 2 block, at most 4 in a line.
How to do it
Method
No 2 × 2 block, at most 4 in a line
4 in a line, one above and one below: a cube
Another way
Fold it in your head
Squares one apart in a line are opposite faces
In full
A cube and a cuboid both have 6 faces, 12 edges and 8 vertices; a cube's 6 faces are equal squares and its 12 edges equal; a cuboid's opposite faces match, and its 12 edges come in 3 sets of 4 equal ones. Opening a solid's faces out flat gives its net. A cube net: has 6 squares; has no 2 × 2 block; has at most 4 in a line; and folds with no two faces landing on each other (two squares with one between them in a line are opposite faces). A cylinder's net is a rectangle and two circles, one on each long side of the rectangle. A triangular prism's net is 3 rectangles in a row with one triangle above and one below (on the same side they would overlap); a square pyramid's net is a square with a triangle on each of its four sides.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A cube's edges are 20 cm long. How many centimetres do all its edges add up to?
Show the answer and working
Answer: 240 cm
A cube has 12 equal edges: 12 × 20 = 240.
Example 2
A cuboid is 8 cm long, 3 cm wide and 11 cm high. How many centimetres do all its edges add up to?
Show the answer and working
Answer: 88 cm
There are 4 edges of each length: 4 × (8 + 3 + 11) = 4 × 22 = 88.
Example 3
The net of a prism with 4-sided ends is made of 6 rectangles and 2 shapes with 4 sides.
True or false?
Show the answer and working
Answer: False
Both ends have 4 sides, and each side of an end joins one rectangular side face: 4 rectangles.
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