## Volume of a CubeIn this section, we will learn the A cube is a three-dimensional solid shape whose length, breadth and height are equal. It has six square faces. Each face of a cube has a side of equal length. Dice is the best example of a cube. The following figure shows the shape of a cube. **Edge:**A-line segment contend with two vertices is called**edge**. There are a total of**twelve**edges in a cube. These edges are of equal length.**Face:**Faces are the square sides of a cube. There are a total of**six**faces (top, bottom, right, left, front, and back) in a cube.**Vertex:**A point where three edges meet is called**the vertex**. There are a total**of eight**vertices in a cube.
## The volume of a CubeThe number of cubic units that a cube occupied is called the ## The Formula of Volume of a cubeMultiply the length (l), breadth (b), and height (h) together to get the volume of a cube. Remember that length, breadth, and height must be The Volume of a Cube (V)=length×breadth×height Or The Volume of a Cube (V)=l×b×h Suppose the length, breadth, and height of a cube is The Volume of a Cube (V)=a×a×a Or The Volume of a Cube (V)=a ^{3}Where:
## When the length of the diagonal is givenSuppose, the diagonal length is d, then the volume of the cube will be: Where:
## Derivation of the FormulaThe space occupied by a solid object is called the volume of that object. We know that all the sides (edges) in a cube are of equal length. Therefore, the formula of the volume of a cube can be derived as follows: - Take a cardboard of square shape.
- Find the area of that cardboard by multiplying length and breadth together.
- As we have taken a square piece of the cardboard, it means the length and breadth will be equal. Suppose, the length and breadth are a, then the
**surface area**of the cardboard will be**a**.^{2} - To get a cubical shape, we will stack multiple cardboard on that piece, one on each other. Now, we can find the height of the cube.
- To get the volume of the cube, multiply the
**surface area**of the cardboard by the**height**. - Form the above steps, we can conclude that the area covered by the cube is the product of the surface area of a square and height.
Let's see how to find the volume of the cube.
Given, side = 9 cm volume (V)=? According to the formula: The volume of a cube (V) = a ^{3}Putting the value of side in the above formula, we get: V= 9
Given, diagonal length (d) = 7 cm volume (V) =? According to the formula: Putting the value of d in the above formula, we get:
Given, volume (V) = 64 cm side (a)=? According to the formula: The volume of a cube (V) = a ^{3}Putting the value of side in the above formula, we get: 64= a
Given, side (a) = 4.5 cm volume (V)=? According to the formula: The volume of a cube (V) = a ^{3}Putting the value of side in the above formula, we get: V = (4.5)
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