Geometry: Finding the Area of a Cube

Updated on December 16, 2018

A cube is a special blazon of rectangular prism where the length, width, and height are all the same. You lot can also recall of a cube as a cardboard box made upward of six as sized squares. Finding the expanse of a cube, then, is quite elementary if y'all know the correct formulas.

Normally, to detect the surface area or book of a rectangular prism, y'all need to work with a length, width, and meridian that are all different. But with a cube, you lot can have advantage of the fact that all sides are equal to easily calculate its geometry and observe the area.

Key Takeaways: Key Terms

  • Cube: A rectangular solid on which the length, width, and height are equal. Y'all demand to know the length, peak, and width to find the surface area of a cube.
  • Surface expanse: The total area of the surface of a 3-dimensional object
  • Volume: The amount of space occupied by a three-dimensional object. It is measured in cubic units.

Finding the Expanse of a Rectangular Prism

Earlier working to find the area of a cube, it's helpful to review how to notice the surface area of a rectangular prism because a cube is a special type of rectangular prism.

A rectangle in three dimensions becomes a rectangular prism. When all sides are of equal dimensions, it becomes a cube. Either way, finding the surface surface area and the book require the same formulas.

Surface Expanse = 2(lh) + 2(lw) + 2(wh)
Book = lhw

These formulas will allow you lot to detect the surface area of a cube, too as its volume and geometric relationships within the shape.

Surface Area of a Cube

Surface Area of A Cube

D. Russell

In the pictured example, the sides of the cube are represented asLandh. A cube has 6 sides and the surface area is the sum of the area of all of the sides. You likewise know that because the figure is a cube, the area of each of the half dozen sides will be the aforementioned.

If you utilize the traditional equation for a rectangular prism, whereSAstands for surface area, yous would have:

SA = half-dozen(lw)

This means that the surface surface area is six (the number of sides of the cube) times the product ofl(length) anddue west(width). Sincefiftyandware represented asLand h, you would have:

SA = 6(Lh)

To see how this would work out with a number, suppose thatL is 3 inches andhis 3 inches. Yous know that50andhhave to be the same because, by definition, in a cube, all sides are the same. The formula would be:

  • SA = 6(Lh)
  • SA = 6(three x 3)
  • SA = 6(nine)
  • SA = 54

So the expanse would be 54 square inches.

Volume of a Cube

Volume of a Cube

D. Russell

This figure really gives yous the formula for the volume of a rectangular prism:

Five = L x W x h

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

L = three inches

W = 3 inches

h = iii inches

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

  • V = L x Due west x h
  • V = 3 10 three x iii
  • V = 27

So the volume of the cube would be 27 cubic inches. Note too 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 ways you are raising the number to an exponent, in this case, the number 3.

  • V = s ^ 3
  • 5 = 3 ^ 3 (which means 5 = 3 10 3 x 3)
  • V = 27

Cube Relationships

Cube Relationships

D. Russell

Because y'all are working with a cube, at that place are certain specific geometric relationships. For example, line segmentAB is perpendicular to segment BF. (A line segment is the distance between ii points on a line.) You also know that line segment AB is parallel to segment EF, something yous tin clearly see by examining the effigy.

As well, segment AE and BC are skewed. Skew lines are lines that are in different planes, are not parallel, and do not intersect. Because a cube is a iii-dimensional shape, line segments AEand BC are indeed non parallel and they practice not intersect, as the image demonstrates.