Non Verbal Reasoning – 2D Views of 3D Shapes (Type 9)

The 2D views of 3D shapes question type requires you to select the correct top down view of the 3D shape given to you. This seems fairly straightforward, all you have to do is work out what the 3D shape looks like from the top.

You will be given a 3D shape with multiple blocks connected in different ways and combinations. The key thing you have to do is visualise how all these blocks would look from a top down perspective. Alongside being aware of the combinations its important to keep track of:

• Number of blocks
• Arrangement of blocks and how they are connected
• Where are the connections
• Which blocks are facing up and which blocks are underneath other blocks
• Where each block is placed
• How the blocks look based on their placement in rows

Just like with other Spatial Reasoning questions, the focus really is on your ability to quickly position and place the blocks based specifically on their top face by using the 3D view you have been given.

To be confident in doing this, it all starts with clearly establishing what the current set of blocks look like now. This question type can be tricky as often the inner blocks and the arrangement of blocks can become confusing. In order to really see what we need to interpret and answer the question, lets have a look at the skills this question type is testing:

• Ability to select only the relevant information
• Ability to identify the faces, points and placement of blocks
• Ability to interpret 3D information into 2D based on specific requirements and characteristics
• Ability to ignore irrelevant information
• Ability to compare 2 different formats to make sure the blocks are in the right number and in the right places
• Working through methodically to make sure the 2D view represents the 3D shape correctly
• Quickly removing inconsistent answer options
• Ability to visual objects from different angles

To summarise, you can probably tell that this question type focuses in on a narrow set of skills when it comes to spatial reasoning all of which follow a logical process. It is not just about how you see visual information differently, but how you can maintain consistency from the 3D shape to the 2D view based on specific characteristics of the overall shape. Those are the things you need to work out. Now, all the mentioned skills can be grouped as the following:

1. Identify the blocks based on the requirements of the questions / instructions
2. Interpretation of the visual information taking into account placement and positions
3. Selection or removal based on consistency / requirements between 2D and 3D

What does the 2D View of 3D Shapes Question Type Look Like?

As you can tell from the CGP example below, the 2D view of 3D shapes question type is in the following format:

• General instructions with an example
• One 3D shape
• Four or five 2D view answer options
• 1 mark per question

How do I select the correct 2D view for the 3D shape?

In order to select the correct 2D view it is important, as already mentioned, to take a step back and understand how you identify that 2D view. You can do this by asking yourself key questions, and focussing on the right elements / parts of the 3D shape. By being clear on what you need to look at you can reduce the chances of getting confused and help yourself build that 2D view.

What you need to be doing here is building your spatial reasoning skills by recognising the position, placement and order of blocks and faces. After recognising these key parts when it comes to the 3D shapes blocks you can then cross-check with the 2D views for consistency.

Think of it as building a set of requirements.

In order to get yourself to a place when can confidently do this, try practise your spatial reasoning skills at home by looking at different objects and, by picking specific parts or elements of them, imagine how they would look from a different angle e.g. top view, bottom view, side view.

Now with all verbal reasoning and spatial reasoning question types there is a method and process you can go through to help you get to the answer. Remember, we want to focus on position, placement, order and consistency and we can do this by asking some key questions through our process. So lets start breaking it down:

1. Read the question and instructions clearly
2. From the 3D shapes blocks identify the blocks which have the top face exposed
3. How many 3D blocks have the top face exposed? Your answer will need to have the same number of blocks, ignore the ones that do not have the top face exposed
4. How many rows (going across) of blocks are there?
5. Go through each row, work out how many blocks are in each row e.g. Row 1 has 1 Block
6. For each block in each row, is it on the left, in the middle or on the right?
7. Look at the answer options, find the options which have the same number of blocks
8. Then find the answers with the same number of rows
9. If you have more than one answer option, from those answers, find the answer which has the blocks in the correct position per row e.g. Row 1 has 1 Block on the Right
10. Make sure to check that the blocks connect correctly e.g. Row 1 Block 1 on the Right connects to Row 2 Block 2 in the Middle
11. Select your answer.

NOTE : One thing to watch out for is whether the answer options have been rotated, this is not common but can happen. In the scenario where the answer has been rotated, identify the rows first, then find one consistent block position and point and use that to help you position all the other blocks (if its easier, rotate the paper!).

Working Example

Now we have a process in place, lets apply it to really see how it works.

First of all it is clear that I have to select the answer option which gives me the top down 2D view of the 3D figure on the left.

Now what is clear here is because I have to look at the top down view, I must only look at the blocks with the top faces exposed. Looking at the 3D block I can see 5 blocks with the top face exposed, I have marked them in red:

What this means is that my 2D top view must only show 5 blocks because, again, only 5 blocks have their top face exposed, the other 2 blocks are hidden underneath.

Now I want to know how many rows of blocks there are, starting with the blocks closest to me. From the 3D view i can see that there are 4 rows. How do I work this out? Well a row is a line of blocks or a block that is either behind or in front of another line of blocks.

From the 3D shape we can see there are 4 lines of blocks.

Starting again from the row closest to me I want to find the number of blocks with the top face exposed per row, remember, only 5 blocks have their top face exposed:

1. Row 1 has 1 Top Face Block Visible
2. Row 2 has 2 Top Face Blocks Visible
3. Row 3 has 1 Top Face Block Visible
4. Row 4 has 1 Top Face Block Visible

Now I know :

1. Row 1 has 1 Top View Block on the Right
2. Row 2 has 2 Top View Blocks – 1 in the Middle and 1 on the Left
3. Row 3 has 1 Top View Block in the Middle
4. Row 4 has 1 Top View Block on the Right

Now I have multiple ways of eliminating the answer options, these are:

1. 5 blocks as there are only 5 blocks with top faces exposed
2. 4 rows of blocks
3. Breakdown of each blocks per row

So let me look at the answer options and use these requirements to eliminate answers. I am doing this because my 2D view answer must be consistent with the 3D shape:

Lets go through each answer option with my first requirement:

1. Answer A has 6 blocks not 5
2. Answer B has 5 blocks
3. Answer C has 5 blocks
4. Answer D has 5 blocks

I know straight away that Answer A cannot be my answer, so I am left with B, C and D.

Lets apply the second requirement of 4 rows:

1. Answer B has only 3 rows of blocks
2. Answer C has only 3 rows of blocks
3. Answer D has 4 rows of blocks

Based on our requirements Answers B and C cannot be the answer as our 3D shape has 4 rows of blocks. Therefore by default Answer D must be our answer – but just to be 100% sure lets apply the last requirement to Answer D:

1. Row 1 (row closest to me) in Answer D has 1 Block on the Right
2. Row 2 has 1 Block in the Middle and 1 Block on the Left
3. Row 3 has 1 Block in the Middle
4. Row 4 has 1 Block on the Right

This layout is consistent with our breakdown that we got from the 3D shape so Answer D must be the answer.

ANSWER : D

To summarise what we have done here is:

1. Identified the number of blocks with the top face exposed / visible – this is important because when looking top down at the 3D shape all we will see are these faces
2. Worked out how many rows of there are with Row 1 being the row closest to me
3. Worked out the number of top face exposed cubes per row
4. Worked out the position of each top face exposed cube or cubes per row e.g. left, middle and right
5. Broke down the position of things starting with Row 1 which is the row closest to me
6. Used a process of elimination to identify the the answer option which is consistent with each of the things we have worked out above

What if I can’t find the answer?

The biggest headache with this question type is translating or seeing the 3D shape into a 2D view with specific requirements e.g. only looking at the top faces of each block. This is where it gets confusing and where you can either miss things out or misinterpret how the 3D shape should look.

This is also why its so important to have a step by step process in place to make sure that what you see in the 3D shape is consistent with the 2D view you select. Now in the situation where you are struggling try the following:

• Only look at the cubes with the top faces visible exposed, ignore everything else
• Always count the number of blocks you see with the top faces exposed, you can begin to eliminate the answer options which do not have the same number of blocks
• Work out the rows or lines of blocks which have their top face exposed / visible and then where each block sits, this will give you an idea of the layout of the 2D view
• Create requirements from what you can see from the 3D shape, but always double check that your requirements are correct
• Cross check the answer options with your requirements, where the options do not fit eliminate them
• Work step by step, at a steady pace
• Draw the layout of the blocks with the top faces exposed / visible, placing them in the right positions
• Where you are still struggling to find the answer you want to take a guess. But this guess must be based on logic and what you can see from the 3D shape, again do your best to create some requirements for the 2D view based on what you see of the blocks with the top faces exposed / visible. Find the answer that best matches what you can see.