Video: Finding the Total Surface Area of a Cube given Its Edge Length

Find the surface area of a cube of length 11 cm.


Video Transcript

Find the surface area of a cube of length 11 centimeters.

To find the surface area of a cube, we need to add the areas of all the faces of our cube. Think about this die for an example. Here is one face, two faces, three faces. This die is a representation of a cube. And a cube actually has six total faces. We can see these faces if we draw a net. A net is a two-dimensional pattern of a three-dimensional figure. We’ve now sketched a net of a cube. The side length of our cube is 11 centimeters. Since this is a cube, every side length will be equal to 11 centimeters.

Back to the question we started with, the question is asking us to find the surface area. To find the surface area, we’ll need to add the area of every face. Let’s start by finding the area of this face. Since we’re dealing with the square face, area will be equal to the side times the side. And for us, that means 11 times 11. 11 times 11 equals 121. But we’re talking about area and we’ve just multiplied centimeters by centimeters, so we said that the area is 121 centimeters squared.

Now what do we know about all the faces of a cube? Each of these faces have the same area. So instead of doing any more multiplication, we can just copy down the area for each face. Each face has an area of 121 centimeters squared. Now we need to add the area of each face together to equal the surface area. We could say the surface area equals 121 plus 121 plus 121, six times. Or, we could use multiplication, since multiplying 121 by six is the same thing as adding 121 plus itself six times.

We multiply 121 by 6. Six times one is six. Six times two is 12, carry our one. Six times one is six, plus one is seven, which tells us that 121 times six equals 726 and tells us that our surface area equals 726 centimeters squared.

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