Volume of a Cube Formula

What is Cube?

A cube is a three-dimensional solid object with six square faces, facets, or sides, three of which meet at each vertex in geometry. The cube is one of the five Platonic solids and is the only regular hexahedron. It is made up of six faces, twelve edges, and eight vertices. The cube is also a right rhombohedron, a square parallelepiped, and an equilateral cuboid. In three orientations, it's a regular square prism, and in four, it's a trigonal trapezohedron. The only convex polyhedron with all square faces is the cube.

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How to Find the Volume of a Cube Formula? 

The three-dimensional space enclosed by a boundary or filled by an object is known as volume. A cube generally has three fundamental dimensions: length, breadth and height. The volume of the cube can be determined by knowing all the fundamental dimensions.

Since the cube has the same dimensions so we can consider the length, breadth and height as equal. Here let us take length, breadth and height as equal to ‘s’.

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Let ‘V’ be the volume of the cube and ‘s’ be the dimensions of the cube. So the volume of a cube formula will be as follows:

V = length × breadth × height

V = s × s × s = s3 cubic units


Steps to Find the Volume of a Cube Formula

  • Take a square sheet of paper as an example.

  • The area occupied by the square sheet will now be its surface area, which is equal to its length multiplied by its width.

  • The surface area of the square will be ‘s2’ since the length and width will be equal.

  • A cube is now created by piling several square sheets on top of one another until the height reaches ‘s’ units. The height or thickness of the cube is denoted by the letter ‘s’.

  • The total area covered by the cube will now be equal to the area of the base multiplied by the height.

  • So, the volume of a cube equation will be V = s × s × s = s3 cubic units.

Volume Formula of Cube and Cuboid

A cube is a three-dimensional figure with equal sides, i.e., all six faces are square. A cuboid, on the other hand, is a three-dimensional figure with non-equal sides and all six faces being rectangles.

The volume formula of cube and cuboid is the same : length × breadth × height. This formula is also known as the formula of cubic meters.


Volume of a Cube Formula When Diagonal is Given

When the three dimensions length, breadth and height are not given for a cube. But the diagonal side value is provided, then the formula to calculate the volume of a cube is as follows:

V = \[\sqrt{3}\]\[\frac{d^{3}}{9}\]

Where V is the volume of the cube and d is the diagonal side of the cube.


Surface Area of the Cube

A solid object's surface area is a measurement of the total area occupied by the object's surface.

The general formula to calculate the surface area of a cube is 

A = 6s2

Where A is the surface area of the cube and ‘s’ is the dimension of the sides of the cube.


Solved Problems

1. Calculate the Surface Area and Volume of the Cube Having the Sides of Length Equal to 8 Cm.

Ans: The surface area of the cube is given by the formula

A = 6s2

Now substituting the values we get the surface area of a cube as follows:

A = 6 × 8 × 8

A = 384 cm2

The Volume of a cube formula is given as follows:

V = s × s × s = s3 

Substituting the values we get the volume of cube as follows:

V = 8 × 8 × 8 

V = 512 cm3.

Therefore, the surface area and volume of a cube having the sides of length equal to 8 cm is 384 cm2 and 512 cm3 respectively.


2. Calculate the Volume of a Cube if the Diagonal of the Cube is Given as 3 Cm.

Ans: The volume of a cube formula when diagonal is given is as follows:

V = \[\sqrt{3}\]\[\frac{d^{3}}{9}\]

Now substituting the values we get the volume of the cube as follows:

V = \[\sqrt{3}\]\[\frac{3^{3}}{9}\]

V = \[\sqrt{3}\]\[\frac{27}{9}\]

V = \[\sqrt{3}\] x 3

V = 3\[\sqrt{3}\] cm3

Therefore the volume of the cube if the diagonal of the cube is given as 3cm is 3\[\sqrt{3}\] cm3.


3. Find the Length of the Edges of the Cube if the Volume of the Cube is Given as 64 Cm3.

Ans: The volume of the cube formula is given as follows:

V = s × s × s = s3 

Since we are given the volume of a cube and we have to find the side of the cube. Let us substitute the values into the formula.

64 = s3

Taking cube roots on both sides of the equation we will get the length of the edges of the cube.

\[\sqrt[3]{64}\] = s

We know that \[\sqrt[3]{64}\] is equal to 4.

So, s = 4 cm.

Therefore, the length of the edges of the cube if the volume of the cube is given as 64 cm3 is 4 cm.


Conclusion

The 3-dimensional space enclosed by a boundary or filled by an object is known as volume. Finding the volume of an object will help us figure out how much water is needed to fill it, such as how much water is needed to fill a container, an aquarium, or a water tank. If we want to decide how much material is needed to cover an object's surface, we must first determine its surface area.

FAQs (Frequently Asked Questions)

1. What is the Formula to Calculate the Volume of a Cube?

Ans: The volume of a cube formula will be as follows:

V = length × breadth × height

V = s × s × s = s3 cubic units

Where V is the volume of a cube and ‘s’ is the dimension of the sides of the cube.

2. What is the Formula to Calculate the Surface Area of a Cube?

Ans: The general formula to calculate the surface area of a cube is 

A = 6s2

Where A is the surface area of the cube and ‘s’ is the dimension of the sides of the cube.

3. What is the Formula to Calculate the Volume of a Cuboid?

Ans: The volume of the cuboid is given by the formula

V =  length × breadth × height.