Surface Area of a Cube



In this lesson, we will learn

  • how to calculate the surface area of a cube.
  • how to find the length of a cube given the surface area.
  • how to use the net of a cube to find its surface area.
  • how to find the surface area of a cube in terms of its volume.
Related Topics: More Geometry Lessons

Surface Area of a Cube

A cube is a three-dimensional figure with six equal square faces. The surface area of a cube is the sum of the area of the six squares that cover it.

cube

The figure above shows a cube. The dotted lines indicate edges hidden from your view.

If s is the length of one of its sides, then the area of one face of the cube is s2.

Since a cube has six faces the surface area of a cube is six times the area of one face.

Surface area of a cube = 6s2

Worksheet to calculate volume and surface area of cubes

 

Example

Find the surface area of a cube with a side of length 3 cm

Solution:

Given that s = 3

Surface area of a cube = 6s2 = 6(3)2 = 54 cm2

The following videos show how to find the surface area of a cube.



Find the length of a cube given the surface area

This video shows how to find the length of a cube given the surface area.



Use the Net of a Cube to find its Surface Area

Another way to look at the surface area of a cube is to consider a net of the cube. The net is a 2-dimensional figure that can be folded to form a 3-dimensional object.

Imagine making cuts along some edges of a cube and opening it up to form a plane figure. The plane figure is called the net of the cube.

The following net can be folded along the dotted lines to form a cube.

net of cube

We can then calculate the area of each square in the net and then multiply the area by 6 to get the surface area of the cube.

There are altogether 11 possible nets for a cube as shown in the following figures. Notice that the surface area of each of the net is the same.

nets of cubes

This video shows how to use nets and 3-dimensional figures to find surface area of cubes and prisms.



Surface Area of a Cube in terms of its Volume

Finding surface area of a cube in terms of volume
S = 6V2/3



You can use the Mathway widget below to practice Basic Math (Finding Surface Area of a Cube) or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.



(Clicking "View Steps" on the answer screen will take you to the Mathway site, where you can register for a free ten-day trial of the software.)





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