A cube has a side length of 12 centimetres. Work out the total surface area of the cube. Give your answer in square metres.
Well, the key point with this question, which is sometimes easy to miss, is the fact that we’ve been given a side length of 12 centimetres. We want the answer in square metres. So therefore, before we start, we want to convert the length of the cube from centimetres to metres because this means that we can give the answer in square metres at the end.
Well, we know that one metre is equal to 100 centimetres. So therefore, if we want to work out how many metres in a centimetre, what we’re gonna do is divide both sides by 100. And that’s because if we want 100 to get down to one, we divide it by 100. And then, we must do the same to the other side. So what we’re gonna get is that 0.01 metres is equal to one centimetre.
And then, in our case, we want to find out how much 12 centimetres is. So what we’re gonna do is multiply each side by 12. When we do that, we get 0.12 metres is equal to 12 centimetres. So therefore, we’ve converted our 12 centimetres into metres.
The other way we could’ve done that straight away is by dividing 12 by 100. And when we divide 12 by 100, it means that all of the digits are gonna move two place values to the right. So, for instance, the one is a ten. So that’s gonna move from the units and then down again into tenths. So that’s why we get 0.12 metres.
Well, the next thing we need to bear in mind is that we’re dealing with a cube. And a cube has a length and width and a height, all exactly the same. So therefore, we can say that the length, the width, and the height overall 0.12 metres. But because it’s a cube as well, we know that the area of each of the faces is going to be identical. So we’re gonna have six identical faces.
So as we have six faces, then to work out the total surface area of the cube, we’re gonna work out the area of one face and then multiply it by six. So what we’re gonna get is 0.12 multiplied by 0.12 multiplied by six. And we get that because the area of the square has the formula 𝐿 squared. So as to work out the area of a square, we just multiply the length by itself.
Because it’s a square, all the lengths are the same. So therefore, when we calculate this, we’re gonna find out the surface area. So like I said, when we do 0.12 multiplied by 0.12, we’re now gonna get 0.0144. And then, this is multiplied by six. So this’s gonna leave us with an answer of 0.0864. And remembering this is metre squared because we want the answer in square metres.
So therefore, we can say that if a cube has a side length of 12 centimetres, the total surface area of the cube is 0.0864 metres squared. Remember, this’s in metres squared or square metres.