A cube is a special type of rectangular prism where the length, width, and height are all the same. Or as lumen puts it: "A cube is a rectangular solid whose length, width, and height are equal." You can also think of a cube as a cardboard box made up of six equally sized squares.

Normally, to find the surface area or volume of a rectangular prism, you need to work with a length, width, and height that are all different. But with a cube, you can take advantage of the fact that all sides are equal to much more easily calculate its geometry. The sections below demonstrate what formulas to use to find a cube's surface area and volume as well as geometric relationships within the shape.

### Surface Area of a Cube

As noted, in a cube, all sides are the same. In the pictured example, you have a cube whose sides are represented as *L *and *h*. You know that a cube has six sides and the surface area is the sum of the area of all of the sides. You also know that because the figure is a cube, the area of each of the six sides will be the same.

If you use the traditional equation for a rectangular prism, where *SA *stands for surface area, you would have:

SA=6(lw)

This means that the surface area is six (the number of sides of the cube) times the product of *l *(length) and *w *(width). Since *l *and *w *are represented as *L *and * h*, you would have:

SA= 6(Lh)

To see how this would work out with a number, suppose that *L* is 3 inches and *h *is 3 inches. You know that *L *and *h *have to be the same because, by definition, in a cube, all sides are the same. The formula would be

*SA = 6(Lh)**SA = 6(3 x 3)**SA = 6(9)**SA = 54*

So the surface area would be 54 square inches.

### Volume of a Cube

This figure actually gives you the formula for the volume of a rectangular prism:

V = L x W x h

If you were to assign each of the variables with a number, you might have:

*L *= 3 inches

*W* = 3 inches

*h* = 3 inches

Recall that this is because all of the sides of a cube have the same measurement. Using the formula to determine the volume, you would have:

*V = L x W x h**V = 3 x 3 x 3**V = 27*

So the volume of the cube would be 27 cubic inches. Note also that since the sides of the cube are all 3 inches, you could also use the more traditional formula for finding the volume of a cube, where the "^" symbol means you are raising the number to an exponent, in this case, the number 3.

*V = s ^*3*V =*3 ^ 3 (which means*V = 3 x 3 x 3*)*V = 27*

### Cube Relationships

Because you are working with a cube, you will have certain specific geometric relationships. For example, line segment *AB* is perpendicular to segment *BF*. (A line segment is the distance between two points on a line.) You also know that line segment *AB* is parallel to segment *EF*, something you can clearly see by examining the figure.

Also, segment *AE *and *BC* are skewed. Skew lines are "lines that are in different planes, are not parallel, and do not intersect," notes Study.com. Because a cube is a three-dimensional shape, line segments *AE *and *BC* are indeed not parallel and they do not intersect, as the image demonstrates.