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Age 11 to 14 Challenge Level:
This problem follows on
from Changing Areas, Changing
Perimeters.
Here are the dimensions of nine cuboids. You can download a set of cards here.
The challenge is to arrange them in a 3 by 3 grid like the one below:
As you go from left to right, the surface area of the shapes must increase.
As you go from top to bottom, the volume of the shapes must increase.
All the cuboids in the middle column must have the same surface area.
All the cuboids on the middle row must have the same volume.
What reasoning can you use to help you to decide where each cuboid must go?
Once you've placed the nine cards, take a look at the extended grid below:
The ticks represent the nine cards you've already placed. Can you create cards with dimensions for cuboids that could go in the four blank spaces that satisfy the same criteria?
Can you design a set of cards of your own with a different cuboid in the centre?
Here are the dimensions of nine cuboids. You can download a set of cards here.
|
1 by 2 by 28
cuboid
|
4 by 4 by 4
cube
|
2 by 4 by 7
cuboid
|
|
1 by 2 by 26
cuboid
|
2 by 4 by 6
cuboid
|
4 by 5 by 6
cuboid
|
|
4 by 5 by 7
cuboid
|
1 by 2 by 24
cuboid
|
1 by 4 by 14
cuboid
|
The challenge is to arrange them in a 3 by 3 grid like the one below:
As you go from left to right, the surface area of the shapes must increase.
As you go from top to bottom, the volume of the shapes must increase.
All the cuboids in the middle column must have the same surface area.
All the cuboids on the middle row must have the same volume.
What reasoning can you use to help you to decide where each cuboid must go?
Once you've placed the nine cards, take a look at the extended grid below:
The ticks represent the nine cards you've already placed. Can you create cards with dimensions for cuboids that could go in the four blank spaces that satisfy the same criteria?
Can you design a set of cards of your own with a different cuboid in the centre?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.