Lesson video

Hi, I'm Miss Davis and in this lesson, we're going to be finding the surface area of cubes and cuboids.

The surface area of any 3D shape is the total area of all of the faces.

Drawing out the neck of the 3D shape can help us to do this.

This is the net of a cube, we'll be using this to find the surface area of a cube.

This cube has got a length of four centimetres, this means that every length on the net is also four centimetres.

We can work out the area of each square by multiplying four by four, this gives us 16 centimetres squared.

Each face of the cube has an area of 16 centimetres squared.

To find the total surface area of the cube, we can multiply this by six as there are six identical faces on a cube.

This gives us an answer of 96 centimetres squared.

Here are some questions for you to try, pause the video to complete your task and resume once you're finished.

Here are the answers, because a cube is made up of six identical faces, you need to find the area of one of the squares and multiply it by six.

This is a cuboid, this is what the net of a cuboid looks like.

Again, we'll be using this to help us work out the total surface area.

This cuboid has length 12 centimetres, 16 centimetres, and three centimetres, I've drawn these onto our net.

There are a lot of the same length, as there are two faces that are of 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 centimetres 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 centimetres squared.

Here are some questions for you to try, pause the video to complete your task and resume once you're finished.

Here are the answers, a cuboid is made up of three sets of two identical faces.

Find the area of the three different pieces and then double it.

Here are some questions for you to try, pause the video to complete your task and resume once you're finished.

Here are the answers, Michaela needs to multiply 101 by two to find the total surface area.

In question four the volume is 512, to find the length of the cube we're find the cube root of 512 which is eight centimetres.

To find the area of each face, we're going to do eight squared which is 64 multiply this by six to get an answer of 384 centimetres squared.

The surface area of this cube is 864 metres squared, this means that the six identical faces add to make 864.

Each face is equal to e squared, as this is e multiplied by e.

There are six faces of area e squared on this cube, we can say that 864, which is the total surface area is equal to six e squared.

First, we're going to divide both sides by six, this means that each face has an area of 144 metres squared.

To find e we're going to find the square root of 144 which is 12, so the length of this cube is 12 metres.

The surface area of this cuboid is 358 centimetres squared, this means that the total area of all of the faces is 358.

The front face is found by multiplying 7 by 12, the side face is found by multiplying seven by u and the top face is found by multiplying 12 by u.

The total surface area can be written like this, as we have two of the front face in the front and the back, two of the side faces on the left and the right and two of the top face, on the top and the bottom.

This simplifies as 168 add 14u, add 24u, this is all added together to give 358 centimetres squared.

We can simplify the right hand side of this equation to give 168 add 38u.

Using inverse operations, we can solve this equation.

The first step is to subtract 168 from both sides, this gives 190 equals 38u, we can then solve that to get u equals five centimetres.

Here are some questions for you to try, pause the video to complete your task and resume once you're finished.

Here are the answers, in Part A the area of each face is 121 meaning the length is 11 centimetres, 11 cubed is 1331 centimetres cubed.

In Part B, we can form an equation which is 166 equals 70 add 10y add 14y this simplifies to give y as four centimetres.

We can then multiply together, five, four, and seven to get the volume as 140 centimetres cubed.

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