Video: Pack 5 • Paper 3 • Question 2

Pack 5 • Paper 3 • Question 2

03:16

Video Transcript

The diagram shows a solid made from seven centimetre cubes. On the centimetre grid below, draw the plan view of the solid.

So each of the individual cubes are one centimetre cubes and there are seven of them. Now, it’s worth just counting them up to make sure you’ve accounted for them all. And we’ve got all seven here. Now, this is important because they could have been a cube, sort of to the left of cube six and behind cube three hidden by cube five in our diagram. But because we’ve accounted for all seven cubes, we know that there isn’t one there.

Now, this sort of diagram is called an isometric view, where you can see the front edge here. And then, the other faces go back at these sorts of angles here. But as well as this 3D isometric view, we can also consider face-on views, like the front elevation. If we were to look at this face of the solid from this direction, what would we see? If we were to look from this direction, we’d call it the side or end elevation.

But this question wants us to imagine we’re directly above the shape, looking straight down on it, and to draw this plan view. And when we do that, this would be the bottom of the shape and this would be the top of the shape.

So looking directly from above at the bottom of the shape, we’d see the top faces of those three cubes, numbers four, five, and six. And they would look like this on the plan view. Then, above those on the left-hand side of our diagram, we would see the top of cubes two and three. So that’s these two squares on the plan. And then, finally, at the top of our plan view, we would see the top face of cube number one. And remember there’s no cube here. So our plan view would look like this.

Now, this visualization of three-dimensional solids from different points of view can be quite tricky. So if you got some little colored blocks and you can put them together, I’d practice doing this. It’s even worth getting your camera out and taking some pictures from different points of view.

So here is our isometric view of the shape that we had. Here’s the front elevation from this point of view. These are the faces we’ll be able to see from that point of view. If we move around to the side elevation, this is what we’d see: the white, yellow, and red blocks on the base layer and the face of the blue above them.

And using this as the base of our plan view, this is what we’d see: the top of the red, blue, and black cubes at the bottom; the yellow and purple cubes above them; and the white cube at the top of our view. So then, this is the answer to the question. This is the plan view.

Now, it’s just worth mentioning that if you’d have taken this as the base of your shape, then this is the plan view you’d have got. If you’d have taken this as the base of your shape, then this is the plan view you’d have got. And if you’d have taken this as the base of your shape, then this is the plan view you’d have got. And all four of these options are correct.

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