 Volume Of A Cube

What is the Volume of a Cube?

Definition: The volume of a cube defines the number of cubic units, that will occupy the cube, completely. A cube is a solid three-dimensional figure, which has 6 square faces or sides. To calculate the volume we should know the dimensions of the cube.

 Volume of Cube = a3

If we know the edge length i.e. “a”, then we can find also find the surface area of the cube. Let us learn how to find the volume of any cubical structure. Volume of a cube

Volume of Cube Formula

We can easily find the volume of the cube (V), by knowing the length of its edges. Suppose, the length of the edges of the cube is ‘a’. Then the V will be the product of length, height, and width. So, the volume of the cube formula is

• Volume of a Cube = Length × Width × Height

= a × a × a

V = a3

where ‘a’ is the length the side of cube or edges.

Derivation for Volume of a Cube

The volume of an object is defined as the amount of space a solid occupies. We know that a cube is a 3-dimensional object whose all the sides i.e. length, breadth, and height are equal. Now for a cube, the volume derivation will be as follows:

• Consider a square sheet of a paper.
• Now, the area that the square sheet will take up will be its surface area i.e. its length multiplied by its breadth.
• As the square will have equal length and breadth, the surface area will be “a2“.
• Now, a cube is made by stacking multiple square sheets on top of each other so that the height becomes “a” units. This gives the height or thickness of the cube as “a”.
• Now, it can be concluded that the overall area covered by the cube will be the area of the base multiplied by the height.
• So, Volume of Cube = a2 × a = a3

What is the Volume of a Cube when Diagonal is Given?

The volume of a cube whose diagonal is given is √3 × d3/9

Thus,

 Volume of Cube From Its Diagonal = √3 × d3/9

Surface Area of Cube

In the same way, we can also find the surface area of a cube, which is basically equal to the number of square units that cover the surface of the cube, completely. The general formula of surface area for a cube of sides, a, is given by;

Surface Area of Cube = 6a2

Example Question Using the Volume of Cube

Question 1: Find the volume of the cube, having the sides of length 7 cm.

Solution:

Given, the length of sides of the cube is 7cm.

We know, Volume of a cube = (length of sides of the cube)3

Therefore, Volume, V = (7 cm)3

V = 343 cm3 is the answer.

Question 2: Find the length of the edges of the cube, if its volume is equal to 125cm3.

Solution:

Given, Volume of the cube = 125 cm3.

Let the length of the edges is a.

We know, by the formula,

The volume of a cube = (length of edges of the cube)3

Substituting the value, we get,

125 = a3

Or a = 3√125

Or a = 5 cm

Therefore, the length of the cube is 5cm.

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What is the relationship of the volume of the cube to its edge length?

The volume of a cube is a3 which means v ∝ a. So, the volume of a cube is directly proportional to its edge.

How many edges and faces are in a cube?

In a cube, there are 12 edges and 6 faces. The surface area of each face is equal and is equal to a2.

Find the edge of a cube whose volume is 125cm3.

V = a3

So, a = √v

Or, Edge (a) = √125 = 5 cm

If the length of diagonal of a cube is 3cm, calculate its volume.

The volume of a cube with respect to its diameter = √3 × d3/9

So, V = √3 × 33/9 = 3√3 cm3.