Find the volume of a cube whose edge length equals nine centimeters.
So, let’s imagine we have our cube. Since it’s a cube, we know that every length will be the same. In this case, they’ll all be nine centimeters long. To find the volume of a cube, we multiply the length times the width times the height. And since all the lengths are the same, we can say that this is the length times the length times the length.
Here, we have the volume equals nine times nine times nine. For our first nine times nine, we can think of this in the same way as finding the area of the front face. If we thought of these as individual one-centimeter cubes, we could say there’d be nine along the bottom and nine up, which would give us 81 cubes in the front face.
And then, we know that we’d have to have nine separate rows of these 81 cubes. So, in our volume calculation, we would continue by 81 times nine. And we can evaluate that as 729. When it comes to our units then, since we’re working with centimeters here with our length of nine centimeters, our volume units won’t just be centimeters. They must be cubic centimeters for the volume. So, the volume of our cube is 729 cubic centimeters.