Cube Volume

The volume of a cube is the sum of the 3-dimensional spaces it occupies. A cube is 3D solid with six square faces, all sides of the same length. Volumes are just the total space occupied by objects. Objects with large volumes occupy more space. Let’s look at the cube volume, along with the formulas and resolved examples in the next paragraph. The unit volume is given as (unit) 3 or as a cube unit. The SI unit of volume is cubic metre (m cube), which is the volume occupied by a cube with a side length of 1 m. USCS units for volumes are inches3, yards3, etc.

The volume of Cube Formula:

You can calculate every dice’s extent using numerous formulations based totally on the given parameters. This may be calculated from the period of the perimeters or the diagonal dimensions of the dice.

What Is Volume of Cube?

The whole 3-dimensional space occupied by a cube is its volume. A cube is a solid 3-dimensional object with six square faces and equal-length sides. One of the five platonic solid shapes is the cube, often known as a regular hexahedron. The (unit)3 or cubic units represent the volume of a cube. The cubic metre (m3) is the volume occupied by a cube with each side 1 metre in length. Inches3, yards3, etc., are the USCS units for volume.

The volume of the cube:

The quantity of space is defined as the object’s volume. As we all know, a cube is a 3-dimensional object with equal length, width, and height on each side. A 3-dimensional closed surface’s volume is the amount of space it contains. The SI unit, the cubic metre, is widely used to measure volume numerically. As a result, a cube’s volume equals x3.

The following steps will help you understand how to calculate the volume of the cube formula. Consider a piece of paper with a square shape. The S.A. of this square sheet is now equal to its length multiplied by its width. The S.A. of a square will be “s2” because the length and width are both equal. A cube is created by stacking many square sheets on top of each other until the height equals the length and width, or “s” units.

As “s,” we get the cube’s height or thickness. As a result, the cube volume will be equal to the area of the base doubled.

Using the Diagonal Formula, calculate the volume of a cube:

If the diagonal is known, another formula can be used to get the cube’s volume directly.

Utilising diagonal to calculate what the volume of the cube is?

A cube’s diagonal is written as 3s, where’s denotes the cube’s side length. ‘s’ can be written as s =diagonal/3 using this formula. Finally, the volume of the cube equation employing a diagonal is cube volume = (3d3)/9, where d is the length of the cube’s diagonal.

Using Edge Length to Calculate Cube Volume

Because the dimensions of all of the cube’s sides are the same, we only need to know one of them to compute the cube’s volume. The side length is used to compute the volume of a cube.

Step 1: Take a note of the cube’s side length.

Step 2: Using the side length, use the following formula to compute the volume: (side)3 = volume of a cube

Step 3: Write the final result and the unit (cubic units) to reflect the volume achieved.

Example: Calculate the volume of a 3-inch-long cube.

Solution: A cube with a 3-inch side length has a volume of (3 3 3) = 27 cubic inches.

Cube Volume Using Diagonal

We may find the volume of the cube given the diagonal by following the procedures outlined below.

Step 1: Take note of the diagonal measurement of the given cube.

Step 2: Using the diagonal, apply the following formula to calculate the volume: [√3×(diagonal)3]/9

Step 3: Convert the result to cubic units.

Calculate the volume of a cube with a three in. diagonal.

Solution:

Diagonal = 9 in

We know that volume of cube is [√3(diagonal)3]/9 and that volume of cube is [√3(3)3]/9 = √3×3 = 3 1.732 = 5.196 in3.

Conclusion

We learned how to define a volume of the cube formula, an example of the cube, and how many faces, edges, and vertices a cube has from the preceding article. The article’s real-life examples and practice questions will aid in your comprehension. A cube or cuboid is a three-dimensional shape with [6,8,12]. The main distinction is that a cube has the same length, width, and height on all sides, whereas a cuboid has varied length, breadth, and height. Both shapes look virtually the same, although they have distinct characteristics. The area and volume of a cube, a cuboid, and a cylinder are all different.