Different Views of 3D Shapes

A shape built from cubes is drawn with an eye beside it. It shows where you are standing, and you pick the option showing that same shape from there.

The shape never moves. It is bolted to the table. Nothing about it is turned, added, taken away or rearranged between the picture and the answer — the only thing that changes is where you are standing. Every question says so in its first line: "The shape does not move — you look at it from…".

That is worth saying twice, because the answers make it easy to forget: each one is the same solid drawn from a different position, so a wrong answer can look exactly like the shape after a turn. It never is. If an option can only be reached by rotating the shape itself, it is wrong no matter how good it looks.

Every answer here is a block shape, never a flat grid. You are always standing at the side of the table, so the shape stays standing up and the answer is that same solid drawn from your new position.

There are only three directions: the left, the right and the back. That is the whole list, and it is worth knowing before you start, because the eye can only ever be in one of three places. "From above" is not asked here — pressing a shape flat onto squared paper is a different question and it has its own type (2D Views of 3D Shapes). "From the front" is not asked either, for a neat reason: the picture you are given is already the view from the front, so the answer would just be the shape copied out.

One warning about the words. "From the left" means the shape's own left side — not the side of the picture nearest your left hand. The eye settles it every time, so trust the eye rather than the sentence. None of our eighteen exam-level questions breaks that rule.

The method

Five beats: say the direction, say what the move does, find your landmark and count to both ends, check the shape, read the bend.

Say the direction. Out loud, off the eye icon, before you look at any option. Left, right or back — there is nothing else it can be. Nearly half the wrong answers are this shape seen from one of the other two, so this one second saves the most marks.
Say what the move does — to you, not to it. Walk a quarter of the way round the table for the left or the right, half way round for the back. The shape has not budged; what changed is which face is nearest you, and so which parts hide behind which. Heights never change, because you walked round the table rather than tipping the shape: what was three cubes tall is three cubes tall from everywhere. That one fact throws out more wrong answers than anything else on the page.
Find your landmark and count to both ends. Most questions mark one block for you — shaded in the shape, ringed in every answer. Four of our eighteen mark nothing, so pick your own: the busiest cube, or the lone one sticking out. Then say two numbers off it. "Two from this end, five from that end." Never stop at "between those two".
Check the shape. Longest run, how many layers, where it bends. Count what the picture actually shows: a cube directly behind another is hidden, so an answer can show fewer cubes than the shape is built from.
Read the bend. Only if the shape has a bend in it. Look along the long arm from its far end. Which way does the next part go? Nothing else catches a mirror.

Beat 3 is the one worth a name: the both-ends count. It beats the near misses.

Give each question 30 to 35 seconds.

💡 Worked example

The shape does not move — you look at it from the right. Which option shows what you would see?

How to answer

Rules to watch

Turn yourself, not the shape. You cannot really walk round a piece of paper, so you do have to picture the move in your head — but picture yourself moving to the new side, not the shape spinning on the spot. The two give the same picture when you get them right and different pictures when you slip, and slipping is the commonest way to talk yourself into a wrong option. Leaning your head really does help.
Left and right are a half turn apart, not a mirror. Walk from one side of the table to the other and you have gone half way round it. A mirror image is a different solid. The flat-picture question type works the other way, so check which one you are in.
Counting decides nothing. All 60 wrong block answers in our exam-level bank hold as many cubes as the right one, and every wrong flat answer is within a single square of it. Counting almost never crosses anything out.
Neighbours decide nothing either. In the example above, the shaded cube touches two others in the right answer — and in all four wrong ones. That is why beat 3 asks for two numbers.
A mirror is not always there. Sixteen of our twenty carry one. The rest look the same both ways round, so no mirror exists. Run beat 5 only when the shape bends.
Expect it to look unfamiliar. The right answer is a drawing you have never seen. That is the question working.

Watch for these traps

We looked at every wrong option in our eighteen exam-level questions.

The view from somewhere else. 34 of the 72, the biggest group by far. A true, careful picture of the right shape — from a direction nobody asked about. Nothing about it looks wrong, because nothing about it is wrong. Only the eye tells you, so ask of each option: from where?
One cube out of place. 24 of the 72. The right view with one cube slid a step along an arm. It can leave the shaded cube with the same neighbours. Count to both ends and it falls over.
The mirror image. 14 of the 72. Every arm the right length, every cube in the right company, and it bends the other way. Your two hands are the same shape mirrored, and no walking round makes one into the other.

Stuck at 30 seconds? Answer on the landmark's distance from one end and move on. Do not start the turn again — the second try usually repeats the first.

Try these yourself

Now have a go yourself — tap the figure that shows that view.

✏️ Question 1

The shape does not move — you look at it from the back. Which option shows what you would see?

✏️ Question 2