Volume

Introduction to Volume

**Introduction to Volume**

Observe the water tanks given below.

How would you decide which one is bigger?

We can do that by observing the space occupied by them or by comparing the maximum quantity of water they can hold.

**The space occupied by a solid shape is its volume, while the maximum quantity of liquid that it can hold shows its capacity. **

We can also say that the capacity of a solid is equal to its volume.

Two-dimensional shapes such as squares and rectangles do not have volume; only three-dimensional shapes have volumes.

**Let us learn the concept by finding the volume of a cube. **

When each side of a cube measures 1 cm, the space occupied by it i.e., its volume is said to be 1 cubic centimetre. This unit is written as c.c. or cm^{3}, which is the fundamental unit of volume. This cube is called the unit cube of side 1 cm.

Now, let us use some unit cubes to a make a bigger cube.

It can be observed that the above cube is made of 27 unit cubes of side 1 cm. Thus, its volume will be equal to the volume of 27 unit cubes.

Volume of bigger cube = 27 × Volume of unit cube = (27 × 1) cm^{3} = 27 cm^{3}

Similarly, we can find the volumes of different cubes or cuboids by virtually breaking them into unit cubes.

**Example 1:**

By using the small cube in figure (a), find the volume of the solid in figure (b).

Figure (a)

Figure (b)

**Solution:**

Volume of smaller cube in figure (a) = 1 cm^{3}

It can be observed that the solid in figure (b) consists of 18 cubes like that in figure (a).

∴ Volume of the solid = (18 × 1) cm^{3} = 18 cm^{3}

**Example 2:**

By using the small cube in figure (a), find the volume of the solid in figure (b).

Figure (a)

Figure (b)

**Solution:**

Volume of the smaller cube in figure (a) = *a*^{3} cubic units

It can be observed that the solid in figure (b) consists of 16 cubes like that in figure (a).

∴ Volume of the solid = (16 × *a*^{3}) cubic units = 16*a*^{3 }cubic units

**Volumes of a Cube and a Cuboid**

Abhinav’s mother gives him a container, asking him to go to the neighbouring milk booth and buy 2.5 L of milk. What does ‘2.5 L’represent? It represents the amount of milk that Abhinav needs to buy. In other words, it is the volume of milk that is to be bought.

After buying the milk, Abhinav notices that the container is full up to its brim. He says to himself, ‘This container has no capacity to hold any more milk.’ What does the word ‘capacity’ indicate? **The space occupied by a substance is called its volu…**

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