# Volume of a Cube

## Method #1 – Volume from the length of one side

### Formula – How to calculate the volume of the cube from the length of one side

Volume = Side3

##### Example

A cube has a side length of 10

Volume = 103 = 10 x 10 x 10 = 1,000

## Method #2 – Volume from the surface area

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

Step 1 – Find the length of one side from the surface area

Side = √(Surface Area ÷ 6)

Step 2 – Find the volume from the length of one side

Volume = Side3

##### Example

A cube has a surface area of 600

Side = √(600÷ 6) = √100 = 10

Volume = 103 = 1,000

## Method #3 – Volume from the perimeter

### Formula – How to calculate the volume of the cube from the perimeter

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

Side = Perimeter ÷ 12

Step 2 – Find the volume from the length of one side

Volume = Side3

##### Example

A cube has a perimeter of 1,200

Side = 1,200 ÷ 12 = 100

Volume = 103 = 1,000

## Method #4 – Volume from the interior diagonal

### Formula – How to calculate the volume 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 volume from the length of one side

Volume = Side3

##### Example

A cube has an interior diagonal of 170

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

Volume = 9.814953 = 945.50597

## Method #5 – Volume from the face diagonal

### Formula – How to calculate the volume 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 volume from the length of one side

Volume = Side3

##### Example

A cube has an face diagonal of 14

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

Volume = 9.899493 = 970.149052