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?

 

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.