फाइंड द वैल्यू ऑफ क्यूब 3 अपॉन 7
Answers
Answer:
What is the Volume of a Cube?
Definition: The volume of a cube defines the number of cubic units, occupied by 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 the volume of the cube. Let us learn how to find the volume of any cubical structure.
Volume of a cube
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
V = 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
Check: Diagonal of a Cube Formula
For More Information On Volumes of Cubes and Cuboid, Watch The Below Video: