The Volume of Geometrical Figures

The volume of an object or a closed surface is a mathematical quantity that shows how often three-dimensional space it occupies. The volume is measured in cubic units such as m3, cm3, and so on.

Volume is sometimes spoken to as capacity. The volume of a cylindrical jar, for example, is used to calculate how much water it can contain.

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Volume of Cuboid

 A cuboid is a solid geometrical object with 6 faces.

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Volume of the cuboid(V) = length × breadth ×  height

Volume of Cube

A cube is a solid geometrical object with 6 faces.

All the sides of the cube are equal in length.

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Volume of the cube(V) = length × breadth ×  height

Volume of the cube(V) = s × s × s (where s is the side of the cube)

Volume of the cube(V) = s3

Volume by Counting Unit Cubes

We know that Volume is defined as a space occupied by a three-dimensional figure.

Let’s understand the concept of counting unit cubes with the help of the following examples:

Example: Find the volume of the given figure. Take the volume of each small cube as 1cm3.

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Solution

Step 1: We have to number the cubes.

A total of 6 cubes are present in the given figure.

So, cubes are numbered from 1 to 6.

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Step 2: Calculate the number of layers in the given figure.

A total of 2 layers are present in the given figure.

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Step3: Calculate the volume of each layer

Volume of layer= (Number of cubes in the layer × volume of small cube)

Volume of layer 1 = 3 × 1cm3 = 3 cm3

Volume of layer 2 = 3 × 1cm3 = 3 cm3

Step4 : Calculate the Total volume

Total volume= Volume of layer 1 + Volume of layer 2 

So, Total Volume of figure = 3 cm3 + 3 cm3

Total Volume of figure = 6 cm3.

Solved Questions

1. Find the volume of the given figure. Take the volume of each small cube as 1cm3.

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Ans: Layer 1 contains 6 cubes,

So, Volume of layer 1 = 6 × 1cm3 = 6 cm3

Layer 2 contains 6 cubes,

So, Volume of layer 2 = 6 × 1cm3 = 6 cm3

Layer 3 contains 12 cubes, (6 in front + 6 in back)

So, Volume of layer 3 = 12 × 1cm3 = 12 cm3

So, Total Volume of figure = 6 cm3+6 cm3+12 cm3

Total Volume of figure = 24 cm3.

2. Find the volume of the cube having side 3 cm.

Ans: Volume of cube(V) = s3

Volume of cube(V) = (3)3

Volume of cube(V) = 3 cm × 3 cm ×  3 cm

Volume of cube(V) = 27 cm3

3.Find the volume of the cuboid having l = 6 cm, b = 4 cm and h = 5 cm.

Ans: Volume of cuboid(V) = length × breadth ×  height

Volume of cuboid(V) = 6 cm × 4 cm ×  5 cm

Volume of cuboid(V) = 120 cm3.

4. What is the volume of the pictures given below. Take the volume of each small cube as 1cm3.

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Ans: For figure A: 

There is a total of 5 cubes

So, the Volume of figure A = 5 × 1cm3 = 5 cm3

For figure B:

There are a total of 12 cubes

(6 cubes in layer 1+ 6 cubes in layer 2)

So, Volume of figure B =  12 × 1cm3 = 12 cm3

Fun Facts:

• When you link two points with only a line segment, you get a one-dimensional object that can only be measured in length.

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• Two-dimensional figures are flat and have two dimensions i.e length and width. The area of a two-dimensional figure can be calculated by using length and width.

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• The objects we come across on a daily basis are solid, three-dimensional objects with the following dimensions: length, width, and depth. The volume for three-dimensional objects is used to estimate their size.

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Summary

In this article we have discussed the concept of volume. First, we discussed volume definition, the volume of cube and cuboid concept and formulas, fun facts, and finally solved the problems. We have learned how to find the volume of figures by counting the unit cubes. 

Learning by Doing

1. Jerry was flying a kite that was yellow in shade. Suddenly, a powerful wind blew, and his kite became tangled in a huge tree. Jerry-built a ladder made of cubical boxes. Now let us count the volume of the ladder to help Jerry in getting his yellow kite. Take the volume of each small cube as 1cm3.

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2. Tim wants to pack his old books in the cubical box. Help Tim in finding the volume of the cubical box on the side 5 cm.

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3. Miss Mary went shopping and bought too many clothes. Now, Miss Mary wants to place all her clothes in her cuboidal cupboard. Let's help Miss Mary in finding the volume of the cuboidal cupboard whose l = 4 cm, b = 3 cm, and h = 6 cm.

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