# Surface Area of a Cube

## Method #1 – Surface area from the length of one side

### Formula – How to calculate the surface area of a cube from the length of one side

Surface Area = 6 x Side2

##### Example

A cube has a side length of 10

Surface Area = 6 x 102 = 6 x 100 = 600

## Method #2 – Surface area from the volume

### Formula – How to calculate the surface area of the cube from the volume

Step 1 – Find the length of one side from the volume

Side = 3√Volume

Step 2 – Find the surface area from the length of one side

Surface Area = 6 x Side2

##### Example

A cube has a volume of 1,000

Side = 3√1000 = 10

Surface Area = 6 x 102 = 6 x 100 = 600

## Method #3 – Surface area from the perimeter

### Formula – How to calculate the surface area of a cube from the perimeter

Step 1 – Find the length of one side from the perimeter

Side = Perimeter ÷ 12

Step 2 – Find the surface area from the length of one side

Surface Area = 6 x Side2

##### Example

A cube has a perimeter of 1,200

Side = 1,200 ÷ 12 = 100

Surface Area = 6 x 102 = 6 x 100 = 600

## Method #4 – Surface area from the interior diagonal

### Formula – How to calculate the surface area of the cube from the interior diagonal

Step 1 – Find the length of one side from the interior diagonal

Side = Diagonal ÷ √3

Step 2 – Find the surface area from the length of one side

Surface Area = 6 x Side2

##### Example

A cube has an interior diagonal of 170

Side = 170 ÷ √3 = 170 ÷ 17.320508 = 9.81495

Surface Area = 6 x 9.814952 = 6 x 96.33324 = 577.9994

## Method #5 – Surface area from the face diagonal

### Formula – How to calculate the surface area of the cube from the face diagonal

Step 1 – Find the length of one side from the interior diagonal

Side = √(Diagonal2 ÷ 2)

Step 2 – Find the surface area from the length of one side

Surface Area = 6 x Side2

##### Example

A cube has an face diagonal of 14

Side = √(142 ÷ 2) = √(196 ÷ 2) = √98 = 9.89949

Surface area = 6 x 9.899492 = 6 x 97.99990 = 587.9994