Volume of a Cube: Overview, Questions, Preparation

In previous classes, you have been taught to identify a square. Now, take 6 such squares and form a 3-D figure.  You get a cube that has a specific surface area and volume. Thus, a cube is a three-dimensional solid with six square faces. 

Source: NCERT

How to calculate the volume of a cube?

The space contained within a three-dimensional object is measured as volume. It is measured in cubic units and it is equal to the number of unit cubes (a unit cube has edges where the side length is 1) that fit inside the object. In the following diagram, each side has a length of 2 units, so two-unit cubes fit along each side. (One unit cube is shaded blue.) 

Source: NCERT

You can calculate the volume of a cube using the formula.
V = S × S × S  
Or,
V = S³. S = length of the side of a cube.

Calculating the volume of a cube using other methods

Variables like the diagonal of a cube, surface area of a square sheet, number of the square sheet, a big cube made of smaller cubes, etc., are also often given to calculate the volume of a cube. In each case, the volume is calculated differently.

For instance, the diagonal of a cube = √3 a,

Therefore, the side of the cube = a/ √3.

Now, using the formula given above for the volume of a cube,
V = (a/√3)³
Therefore, V = √3a³ / 9.
Similarly, if there are some square sheets kept one above the other with a side measuring 5 cm, and there are 5 such sheets, the volume of the cube thus formed will be:
V = surface area of a sheet' number of such sheets
In this case, 
V = 5² × 5 = 125 cm³.
When a big cube is made by joining several unit cubes, the volume of the cube is calculated by calculating the side of the new cube, and then the standard formula used to calculate the volume of a cube is applied. For instance, if a cube is made of 4 unit cubes, the side of the big cube will be 2 cm. Therefore, the volume is 2³ = 8 cm³.

This chapter, Mensuration, is taught in the 10^th standard.
Along with volume, concepts like surface area, lateral surface area, and diagonal of different shapes are also taught in this chapter. It carries around 5-7 marks. 

1. Find the volume of a cube with a side 6 cm.
Solution.

Side = 6cm, therefore,
Volume = 63 = 216 cm³.

2. The volume of a cube is 64 cm3. What is the value of its side?
Solution.

Volume = a³ = 64 cm³.
Therefore, a = ∛64 = 4 cm.

3. A cubical tank of water can hold 729000 ml of water. Find the measurement of the side of the cubical tank.

Solution.

We know, 1 ml = 1 cm3.
Therefore, side of the cubical tank = ∛729000 cm³ = 90 cm. 
Thus, each side of the cubical tank is 90 cm.

Q: Give some examples of a cube in reality.

Q: Difference between diagonal of a square and diagonal of a cube.

Q: Is the angle at every corner of a cube the same as a square?

Q: What is the surface area of a cube?

Q: What is the significance of the chapter?