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The Volume of Cube

The total variety of cuboid units occupied by a cube is outlined because of the volume of the cube. A cube may be a solid three-dimensional form with six sq. faces. The total space occupied by an object is defined as its volume. The volume of a thing determines how much space it takes up. In the parts 

that follow, we’ll go through the volume of a cube in detail, including the formula and examples.

What is a volume of a cube?

The total three-dimensional space occupied by a cube is its volume. A cube is a three-dimensional solid object with six square faces and equal-length sides. One of the five platonic solid shapes, the cube is also known as a regular hexahedron. The volume of a cube is expressed in (unit)³ or cubic units. The cubic meter (m³) is the SI unit of volume, and it is defined as the volume occupied by a cube with each side measuring 1 meter. Inches³, yards³, and so on are the USCS units for volume.

The volume of Cube Formula:

The volume of any cube can be measured using different formulae based on the given fundamentals. By using the side length or the measure of the cube’s diagonal the volume of a cube can be measured.

The volume of Cube using Side Formula:

volume of a cube can be multiplied by the length of the edges by three times. For example, if the length of a cube’s edge is 4, the volume is 4³. The formula for calculating a cube’s volume is the Volume of a cube = s³, where ‘s’ is the length of the cube’s side.

The concept of obtaining the volume of a cube formula can be understood using the following steps,

  • Take any square-shaped piece of paper as an example.
  • The area covered by this square sheet is now its surface area, which is equal to the length multiplied by the width. Because the length and width of a square are equal, the surface area is “s³ .”
  • A cube is formed by stacking many square sheets on top of each other until the height equals the length and width, resulting in “s” units.
  • The height or thickness of the cube is denoted by the letter “s.”

As a result, the entire space covered by the cube, or volume, will be equal to the area of the base multiplied by the height.

The volume of Cube Using Diagonal Formula

The volume of the cube can also be found directly by another formula if the diagonal is known. The diagonal of a cube is written as 3s, where ‘s’ is the cube’s side length. We can write ‘s’ as s = diagonal/3 using this formula. As a result, the volume of a cube equation with a diagonal may be written as: Volume of the cube = (√3×d)/9, where d is the length of the cube’s diagonal.

Note: Don’t confuse the diagonal of a cube with the diagonal of its face to avoid making a common mistake. As demonstrated in the diagram above, a cube’s diagonal cuts through its center. The face diagonal, on the other hand, is the diagonal on each of the cube’s faces.

How To Find the Volume of a Cube?

The volume of a cube can be easily found by just knowing the length of its edge or the measure of its diagonal. Different steps to be followed to calculate the area of the cube depending on the given parameters will be covered in this section.

The volume of Cube Using Edge Length

The measure of all the sides of a cube is the same thus, we only need to know one side to calculate the volume of the cube. The steps to calculate the volume of a cube using the side length are,

  • Step 1: Measuring the side length of the cube and writing it down.
  • Step 2: Apply the formula to calculate the volume using the side length: Volume of cube = (side)3.
  • Step 3: Expressing the final answer along with the units(cubic units) to represent the obtained volume of a cube.

Example: The volume of a cube can be observed with a side length of 2 inches.

Solution: The volume of a cube with a side length of 4 inches would have a volume of 

(4 × 4 × 4) = 64 cubic inches.

Therefore, it can hold a total of 64 cubes of 4 inch each.

Volume of Cube Using Diagonal

Given the diagonal, we can follow the steps given below to find the volume of a given cube.

  • Step 1: Write down the measurement of the diagonal of the given cube.
  • Step 2: Apply the formula to find the volume using diagonal: [√3×(diagonal)3]/9
  • Step 3: Write down the derived result in cubic units.

Example: Calculate the volume of a cube with the diagonal measuring 3 in.

Solution:

Given: Diagonal = 9 in

We know, volume of cube = [√3×(diagonal)3]/9

⇒ Volume = [√3×(3)3]/9 = 3 × √3 = 3 × 1.732 = 5.196 in3.

Important Notes:

The formulas to find the volume of a cube is:

  • V = s3, where s indicates the edge length of the cube.
  • V = √3×d3/9, where d indicates the diagonal length of the cube.

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