Lesson video

Hello, my name is Dr.

Rowlandson.

I'm delighted that you'll be joining me in today's lesson.

Let's get started.

Welcome to today's lesson from the unit of plans and elevations.

This lesson is called Drawing the Solid from the Plan and Elevations.

And by the end of today's lesson that is exactly what we'll be able to do.

We'll be able to draw a solid based on its plan and elevations.

Here are some previous keywords that will be useful during today's lesson, so you may want to pause the video if you need to remind yourself what any of these words mean and then press play when you're ready to continue.

This lesson is broken into two learning cycles.

In the first learning cycle, we're going to be drawing solids that are made out of cubes.

And then the second learning cycle, we're going to draw different solids.

Let starts off with drawing solids made from cubes.

Here, we have Andeep and his friends.

Andeep makes a solid out of cubes and hides it from the others.

He shows them all the front elevation of his solid and each of them then tries to make a solid of their own outer cubes to try and match Andeep's.

They look a bit like these.

It looks like the three of these people, the front elevation of the solid does match Andeep's, but for one of them it does not, Which solid will definitely not match Andeep's solid then? Pause the video while you think about this and think about why as well.

And press play when you're ready to continue.

It looks like Izzy's solid will not match Andeep's 'cause the front elevation is not the same.

There is an extra cube on top of Izzy's that cannot be seen in Andeep's.

So, Andeep shows the rest of them the side elevation of his solid.

Now, it looks a bit like what we can see here.

Now none of them knew what the side elevation looked like when they built their own solids, but based on this new information, which solid will definitely not match Andeep's solid now? Pause video while you think about this and think about why as well, and press play when you're ready to continue.

It looks like Sofia's solid would not match Andeeps now because it's missing a cube from the back of it.

And then, Andeep shows the plan of his solid.

It looks a bit like what we can see on the left.

Once again, Jacob and Jun, they didn't know what the plan looked like when they made the solid, but based on what you can see now, which solid will definitely not match Andeep solid this time? Pause video while you think about this and press play when you're ready to continue.

It looks like Jun's solid won't match Andeep's this time because he has an extra cube on it which cannot be seen from the plan view of Andeep's.

So, Andeep shows all three viewpoints of his solid and says, "Well done Jacob! Your solid matches mine." Jacob's solid has the same front elevation with four squares arranged in an L, has the same side elevation with four squares arranged in that way and the same plan with five squares arranged in an L shape there as well.

Let's check what we've learned.

Andeep makes another solid outer cubes and hides it from the others.

He shows them all the plan of his solid.

They each make a solid outer cube to try and match Andeep's solid.

Which solid or solids will definitely not match Andeep's solid based on this information? Pause video while you choose and press play when you're ready for an answer.

Jun's and Jacob's will not match Andeep's solid.

If what Andeep had shown had been the front elevation, then it would.

But he hasn't shown that, he's shown the plan.

Therefore, Jacob and Jun, their solids will not match.

So, we're left now adjust with Sofia and Izzy.

Andeep shows the remaining people the side elevation of his solid.

Based on this information which solid will definitely not match Andeep's solid? Pause video while you choose and press play when you're ready for an answer.

Sofia's solid would not match Andeep's because there's a cube missing from it.

You'll be able to see four squares from the side elevation, but Sofia's can only see three.

Here we have Alex who has drawn a solid on isometric paper based on the front elevation, side elevation, and plan.

Now, this is quite tricky to do because you can't see all the solid in one go.

You could try and imagine what the solid looks like based on the front elevation, side elevation and plan, and create a mental image of the solid and then draw it based on your mental image.

Or you could draw a solid based on one piece of information and then adjust it based on the other piece of information one at a time by drawing extra line segments and rubbing things out.

Let's see what Alex does.

Alex says, "I'll start by imagining what the solid could look like based on just the front elevation.

I could even draw this out." For example, this solid would have the same front elevation as what we can see.

He then says, "I'll use a side elevation to adjust my mental image or adjust my drawing." So, what we can see here is the solid he's drawn already has a side elevation of just two squares, but we want a side elevation of three squares so we can adjust it like this and now it matches both the front and the side elevations.

It then says I'll make one final adjustment based on the plan.

Currently, in the plan view of this solid, you would see four squares arranged in an L shape, but the plan actually has six squares, so we need to add two more cubes, but we need to add 'em in a place that you wouldn't be able to see from the front elevation or the side elevation because those elevations are already correct.

They would have to go here.

Aisha and Sam each construct a solid out of cubes based on the front elevation, side elevation and plan, what we can see here on the left of the screen.

Let's see what they make.

They make these.

They're similar but also a little bit different.

Aisha says, "I've used more cubes than Sam." So, are they both correct? Does each solid match the front elevation, side elevation, and plan from what we can see on the left? Pause video while you think about this and press play when you're ready to continue.

Yes, they both do.

Let's take a look why.

Both solids have the same front elevation.

They both match to one on the left.

They both have the same side elevation as well and they both have the same plan.

So, how are they different? The cubes that differ between these two solids cannot be seen from either the front elevation, the side elevation, or the plan.

It's these cubes here.

That means the plan and elevations do not show every aspect of a solid such as features inside it.

You may sometimes need more information in order to construct a solid perfectly accurately.

Let's check what we've learned.

Here, you've got the front elevation of a solid.

Draw a solid that has the same front elevation as this one and you may use isometric paper to help you.

Pause video while you do that and press play when you're ready to see an answer.

Here is the possible answer.

You could just draw two cubes, one above the other.

You can have more cubes than that so long as they are hidden behind these two cubes.

Needs to be behind it going off to the right, for example.

Now, you've got a front elevation and a plan.

Draw a solid that has a front elevation and plan which match these ones below.

And once again you may use isometric paper to help you.

Pause video while you do that and press play when you're ready to see a possible answer.

Here is what a possible answer could look like.

This has the same front elevation, it has two squares above each other, and the same plan, three squares in a line.

Yours might differ depending on where that extra cube is.

It could be in any of those places across the top or it could even be in any place underneath.

So, now you have the front elevation, plan, and side elevation.

Could you please draw a solid that matches all of these? And once again you may use isometric paper to help you.

Pause video while you do that and press play when you're ready to see an answer.

Here's our answer.

Does yours match this one? If so, well done.

Okay, it's over to you now for task A.

This task contains three questions and here is question one.

You have a front elevation given to you here and what you need to do is draw at least three different solids that have the same front elevation as this one here and you can use isometric paper to help you if you'd like to.

If you've drawn three, you may want to try and draw more if you'd like to as well.

Pause video while you do this and press play when you're ready for question two.

And here is question two.

You have a front elevation and a side elevation, and this time you need to draw at least two different solids that have the same front elevation and side elevation as what you can see here.

Pause video while you do this and press play when you're ready for question three.

And here is question three.

You have a front elevation, a side elevation, and a plan.

And what you need to do is draw a solid that has the same plan and elevations as what you can see.

Pause video while you do this and press play when you're ready to start looking at some answers.

Let's take a look at some answers.

So, for question one, you only have the front elevation.

There are lots of different options you could draw for a solid for this.

Here are some examples of answers.

Yours might look like any of these, they might not do, might have something a bit different, but what you're looking for is that from the front elevation you would be able to see five squares arranged in that same way.

Pause video while you check yours or if you have someone else who can help you, ask them to check it as well.

And then press play when you're ready to continue.

And then question two, we have a front elevation and side elevation.

Once again, there are different options, but you could have any of these or you may have different things.

Pause video while you check yours against these and check if you have anything different.

Maybe just double check they have the same front elevation and side elevation or ask someone else to check it for you.

Then press play when you're ready for question three's answer.

And in question three, we have front elevation, side elevation, and plan.

You can have this solid or a reflection of it.

Pause while you check yours and then press play for the next part of today's lesson.

You're doing great so far.

Now, let's move on to the next part of this lesson, which is drawing different types of solids.

A solid can be built from its plan, front elevation, and side elevations.

For example, you can make it out of cubes if it suits that or you can make it out clay or other building materials instead.

A sketch of a solid can also be drawn from its plan and elevations as well.

Now, a sketch doesn't have to be drawn perfectly accurately.

Sketching solids is a quick way of visualising a shape without spending too much time constructing it with a precise level of accuracy.

Sketches do not need to look perfect, but they should be a clear representation of what the solid is and should appear relatively in proportion.

In other words, things that are along with other things on the actual side should be like that as well in your sketch.

This can be done by using a ruler to measure outside lengths and also by paying attention to sides which should be parallel to each other in your sketch.

Let's look an example together.

The diagram shows the plan, front elevation, and side elevation of a solid drawn on a centimetre square grid.

And what we need to do is draw a sketch of the solid, showing the lengths of the solid on our sketch and Lucas is going to help us.

Let's see what he does.

He says, "I'll start by drawing the front face, which is a trapezium." And he does it like this.

He uses the squares on the grid to help him write down the length of the trapezium.

He then says, "I'll use the side elevation to draw the face that's at the side, which is a rectangle." And he draws it like this, with five centimetres going backwards in its depth.

He says, "Even though the perspective of my sketch means it doesn't look like a rectangle, the shape drawn represents the rectangle face of the solid.

I should check that relevant edges are parallel to each other." So for example, these edges on the side elevation are parallel to each other.

They should be parallel to each other in the sketch as well.

These edges in the side elevation are also parallel to each other and they should be parallel to each other in the sketch as well.

You might be thinking about this rectangle and thinking about how it's five centimetres across, but it shouldn't be three centimetres up like it is on the side elevation because the height of the trapezium is three centimetres, which means it's slope length will be longer.

So, surely this rectangle should be five centimetres by something that is longer than three centimetres.

Well, Lucas is gonna help explain this to us.

He says, "The height of the rectangle in the side elevation is three centimetres, but the length of the actual rectangle is greater than three centimetres because it's a sloped length." He says, "I don't necessarily need to work out what this length is unless I'm asked to." If you imagine taking a rectangle, for example, you could hold a book up in front of you and then tilt that book so that it is tilting away from you, even though the book is still the same length, the amount of space in your field of vision it takes up would be less.

And that's what's going on with this rectangle here.

It is longer than five by three, but it appears five by three from a side elevation.

Lucas then says, "I'll now use the plan to draw the top face." He says, "The highlighted rectangle is the view from above of this sloped rectangle that I've already drawn." So, that one has already been done.

He says, "I need to draw this rectangle which shares an edge with the top of the trapezium." This side here.

Well, the four centimetre side is already drawn, so he needs to draw the five centimetre side like this.

He says, "The other rectangle is a face that I cannot see from this point of view on my sketch." 'Cause it would go here.

He says, "Again, I can check for all the relevant edges, which I can see are parallel to each other." So, these should be parallel and so should these.

He says, "I'm finished.

It's a trapezium prism." Let's check what we've learned.

The diagram shows the plan, front elevation, and side elevation of a solid drawn on a centimetre square grid.

Draw a sketch of the solid showing lengths of the solid on your sketch.

Pause a video while you do this and press play when you ready to see an answer.

Here's our answer.

It is triangular prism.

The front elevation is a triangle, which is six centimetres across and a height of three centimetres.

The side elevation is a rectangle.

We don't necessarily know how long that rectangle is, but we know from this point of view, its height is three centimetres and it goes backwards five centimetres.

And from the plan of view, you can see two rectangles, which you can see there.

Now, one of them in your sketch cannot be seen and that's absolutely fine.

Let's take a look at another example now.

The diagram shows the plan, front elevation, and side elevation of a solid drawn on a centimetre square grid.

And what we want to do is draw a sketch of a solid showing the length of the solid on there.

The plan is a circle, the front elevation is a rectangle, and the side elevation is a congruent rectangle.

Laura's will help us out with this one.

Let's see what she says.

She says, "It can sometimes be helpful to work out what the shape the solid is before starting the sketch." Can you imagine what shape this is? Pause video while you think about it and press play when you're ready to continue.

Take a look together.

Laura says, "From above, you can see a circle.

Some circular solids include cones, cylinders, and spheres." She says, "Both the front and side elevation are congruent rectangles.

Now, a cylinder would satisfy both of these." So, let's now draw this together and let's start with the plan and draw what should be a circle.

It doesn't look like a circle does it, with the way we've drawn it? Laura says, "The perspective makes it look like an ellipse, but it represents a circle with a radius of three centimetres." That's what we're trying to do here.

We're trying to create a 2D representation of this 3D shape.

The radius is three centimetres, we can mark it on.

She then says, "I'll now draw two parallel lines for the edges of the rectangle that can be seen from the front." And those parallel lines should be four centimetres.

The height of the front elevation is equal to the height of the cylinder, so are the four centimetres.

She then says, "I'll now draw the curve at the base of the cylinder, like so." She says, "This would be longer than the base of the rectangle." The curve part would be because directly across from one to the other is six centimetres.

Laura says, "The sketch is complete.

The side elevation would be the same as the front elevation." So, let's check what we've learned.

The diagram shows the plan, front elevation, and side elevation of a solid drawn on a centimetre square grid.

Draw a sketch of the solid showing the lengths on the solid.

Pause video while you do this and press play when you're ready to see an answer.

You should draw a cylinder that looks something a bit like this.

You may label the diameter as two centimetres or the radius as one centimetre.

Okay, it's over to you now.

For task B, this task contains five questions and here is question one.

You're shown the plan, front elevation, and side elevation of a solid on a centimetre square grid.

And what you need to do is sketch the solid, showing the dimensions of the solid on your sketch.

Pause video while you do it and press play when you're ready for question two.

And here is question two.

Same task again, but a different plan, front elevation, and side elevation.

Pause while you do this and press play for question three.

And here is question three.

It looks very much like question two, but just slightly different.

Draw a sketch of this solid.

Pause while you do this and press play when you're ready for question four.

And here is question four.

Again, similar to question three, but a little bit different.

Draw a sketch of this solid.

Pause while you do this and press play when you're ready for question five.

And now for something a little bit different.

Question five is a different look in solid.

Pause video while you do this and press play when you're ready to go through some answers.

Okay, let's take a look at some answers.

For question one, you should draw a triangular prism that looks a bit like this.

And question two, hopefully you drawn a cylinder that looks something a bit like this.

You may have put the diameter is four centimetres or the radius is two centimetres.

It's up to you.

For question three, it looks very much like the last one apart from rather than seeing rectangles from the front and side, we see triangles.

And we also have that point in the middle of the circle, the plan.

That's because this is a cone and it should look something a bit like this.

And then question four, it looks somewhere in between the cylinder we saw and the cone.

We also have a circle inside a circle.

I wonder why that might be.

It should look something a bit like this, a frustum.

It is like a cone with the top of it chopped off.

Then finally, question five, the plan, front elevation, side elevation are all made out of rectangles or rectilinear compound shapes, which means our solid would be made out of cuboids.

It would look something a bit like this.

Fantastic work today.

Now, let's summarise what we've learned during this lesson.

A solid can be built from its plan, front elevation and side elevation.

All three pieces of information are needed to construct a solid.

However, multiple solids can have the same plan, front elevation, and side elevations.

So, these piece of information do not tell you enough about what goes on inside a solid.

So, you may need more information in order to construct it perfectly accurately.

Well done today.

Hope you have a great day.