Non-verbal reasoning: Cubes and nets: an introduction A net is a 2D figure which can be folded into a 3D object. The net of a cube will, when cut out and assembled, make a cube! Look at the nets below. Which of them is the net of a cube? Cut them out and try to assemble them if you need to.
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Only the blue net will make a cube.
Now it’s time for some colouring, cutting and sticking. Using the net below, make a selection of cubes. Before you stick them together to make them 3D, draw different patterns or shapes on some of the sides.
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Pick one of your nets, and draw different 3D views of it. As you can see, you’ll only be able to see some of the sides and elements you’ve drawn at any one time. Here’s an example to show you:
In these non-verbal reasoning questions you will need to relate a 2D net to the cube that can be made out of it. As always, this takes a fair amount of practice, but these tips will help: above blue circle Use the front of the cube as an anchor and try to fix what goes above and to the sides, based on the net.
front of cube
underneath the blue circle
Remember, alternate squares on the net cannot be adjacent (next to each other) on the cube.
right of the blue circle
Alternate squares
Alternate squares
CUBES AND NETS EXERCISES 1-8 Choose the cube on the right that can be formed from the net on the left. 1
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Answers: 1
Were you fooled by the trick question? D cannot be the correct answer, because the 3D view of the cube would not show two adjacent black sides. In answer C the hatched side is hidden, and we can see two white sides and a black side.
2
There is only one black side on the net, so we can use it as our anchor. In cubes B, C and D the black side is adjacent to a side that doesn’t appear in that position on the net, and cube E has hatching that doesn’t appear on the net at all. The answer must be A.
3
Use the triangle side of the cube as your anchor and work your way from left to right discounting options. If the triangle is pointing up, could the cube have adjacent black and grey sides? Yes - so option A is our answer.
4
Using the black side as an achor, work your way through the options. We can discount D immediately (two black sides, when the net only has one). In options A, B and E the grey side is adjacent to the black, but that’s not possible with this net. The correct answer is C.
5
We can discount any cubes with side patterns that don’t appear on the net (A, D) and discount option E (the net doesn’t have three white sides). Option B would be possible, so that is the correct answer.
6
Working from left to right we can immediately discount A (black, grey and white sides could not be adjacent with this net). Using the black rectangle shape as our anchor side we see that it does correspond to the net (remember to ‘line up’ the rectangle shape vertically when you’re visualising the 3D cube!).
7
Use the F side of the cube as your anchor (remember to match the orientation, though!). The two most likely options are A and E, as they both have an F side, so check them first. A can be discounted because the black side is on the left of the cube, not the right. All the sides on the E cube are in the correct position, so that is the right answer.
8
Use the white side of the cube as your anchor to find the correct net, C.
