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The example above of dimensions 2 by 3 by 4 uses exactly 36 rods and has a volume of 24 cube units.
Find all the cages that have a volume of 20 to 25 cube units inclusive and use 40 to 50 rods inclusive.
The example above of dimensions 2 by 3 by 4 uses exactly 36 rods.
This sheet contains a copy of the task.
Wire Cages
Age 7 to 14
Challenge Level 
You may wish to look here at a 2D task which could be explored before this 3D task.
Wire cages are used to contain large rocks in some building projects.
Here is a small version of a 2 by 3 by 4 wire cage cuboid, made with plastic straws.
We can see 14 red rods of length 2 units, 12 blue rods of length 3 units and 10 green rods of length 4 units.
For all the challenges below, no rod is allowed to be longer than 6 units and each cage is always a cuboid.
Challenge 1
The example above of dimensions 2 by 3 by 4 uses exactly 36 rods and has a volume of 24 cube units.
Find all the cages that have a volume of 20 to 25 cube units inclusive and use 40 to 50 rods inclusive.
Challenge 2
The example above of dimensions 2 by 3 by 4 uses exactly 36 rods.
Can you find a cuboid that uses exactly 28 rods?
Can you find all the cuboids that use exactly 28 rods?
Can you find all the cuboids that use exactly 28 rods?
Challenge 3
Find at least one pair of cuboids of different dimensions, that when constructed:
- Use exactly 100 rods
AND
- Have each dimension greater than 2 rods.
- Use exactly 100 rods
AND
- Have each dimension greater than 2 rods.
This sheet contains a copy of the task.