Lesson video

Hi, I'm Miss Davies.

In this lesson, we're going to be calculating the volume and surface area of composite solids.

These are 3D shapes that are formed using two or more 3D shapes.

Let's start by recapping cuboids.

To find the volume of a cuboid, we multiply the width by the height, by the length.

The width of this cuboid is 4.

2 metres, the height is 1.

5 metres, and the length is eight metres.

These multiplied together to give us an answer of 50.

4 metres cubed.

This cuboid has lengths, 12 centimetres, 16 centimetres, and three centimetres.

I drawn this onto our net.

There are a lot of the same lengths as there are two faces that are this size, two of this size, and the final two, are also the same.

I've labelled these as A, B and C.

Let's start by finding the area of face A.

To do this, we're going to multiply 12 by 16.

This gives us 192 centimetres squared.

So this is 192, and this face, is also 192 centimetres squared.

Next, let's work out the area of faces labelled B.

These faces are three centimetres by 12 centimetres.

To work out the area, we'll do 12 multiplied by three, which is 36 centimetres squared.

This face is 36 centimetres squared, and this face is also 36 centimetres squared.

Finally, let's work out the area of the faces labelled C.

These have lengths, three centimetres and 16 centimetres.

The total area of these faces, is 48 centimetre squared each.

To find the total surface area of this cuboid, we're going to add together all of the areas.

We have got two lots of 192, two lots of 36 and two lots of 48.

This gives us a total surface area, of 552 centimetre squared.

Here there're some questions for you to try.

Pause the video, to complete your task and resume once you're finished.

Here are the answers.

To calculate the volume of this composite solid, you could have split this into two cuboids worked out the volume of each of the cuboids and added this together, or you could have found the area of the cross-section which is the L-shaped front and multiplied it by the lengths.

Next, let's recap triangular prisms. To find the volume of a triangular prism, multiply the width by the height, by the length and divide by two.

The width of this triangular prism is 12, the length is 20, but what is the height? It is five metres, as the nine metres is a diagonal length, whereas five metres is the length which is perpendicular to the base.

This gives us an answer of 600 metres cubed.

This net will help us working out the surface area of the triangular prism.

Let's start by labelling all of the sides.

We can now begin to work out the surface area of the triangular prism.

I have color-coded and labelled the different sized faces of the prism.

To find the surface area of the triangular prism, we're going to calculate the area of each face.

Let's start with face A.

The area of face A is found by multiplying seven by six, to give 42 centimetres squared.

Face B is found by multiplying seven by eight.

This gives an area of 56 centimetres squared.

Face C, is found by multiplying seven by 10.

So face C have an area of 70 centimetres squared.

To find the area if the faces that are labelled D, going to multiply six by eight and divide by two.

This gives 24 centimetres squared.

This means that both the faces that are labelled D, have an area of 24 centimetres squared.

To find the total surface area of the triangular prism, we need to add the area of each of the faces together.

This gives 216 centimetre squared.

Here there's some questions for you to try.

Pause the video, to complete your task and resume once you're finished.

Here are the answers.

Like in the previous question, you could have found the volume by either calculating the volume of the cuboid and the triangular prism separately and adding them together, or you could have found the area of the pentagon cross-section and multiplied it by the length.

That's all for this lesson, thanks for watching.