Volume Formula

What do children’s blocks, an ice-cream crate, and dice have in common? What is unique about the shape of the sides? Each of these objects is an example of a perfect cube. A cube is a three-dimensional shape that has squares for all six of its sides. So, how anyone finds out how big a cube is? This can be done by finding the object’s volume. The volume of any cube can be computed as the amount of space the cube takes up or as the amount of space inside of the cube. In this article, we will explore the volume formula of various objects with different shapes. Let us learn a new thing.

Volume Formula

What is Volume?

For a solid object, the space occupied by such an object is measured and is termed as the volume of the object. Also, if the object is hollow, then the interior is empty. This can be filled with air or some liquid. In this case, the volume of the substance that can fill the interior will give the capacity of the container.

Therefore, the volume of an object is the measure of the space it occupies or the capacity of an object is the volume of substance its interior can accommodate. Here, the unit of measurement of either of the two is the cubic unit.

Various Volume Formulae:

The volume of different objects with different sizes and shapes will be calculated as follows:

1. The volume of a cuboid:

V = l × b × h

Where,

V	Volume of Cuboid
l	Length of Cuboid
b	Breadth of Cuboid
h	Height of Cuboid

2. The volume of a cube:

V = a³

Where,

V	Volume of Cube
a	Side of Cube

3. The volume of a Cylinder is:

V= \(\Pi × r^2 × h\)

Where,

V	Volume of Cylinder
r	The radius of Circular Base
h	Height of Cylinder

4. The volume of a Sphere is:

V = \(\frac{4}{3}× \Pi ×r^3\)

Where,

V	Volume of Sphere
r	Radius of Sphere

5. The volume of a Right circular cone:

V = \(\frac{1}{3}× \Pi ×r^2 × h\)

Where,

V	Volume of Cone
r	The radius of Circular Base
h	Height of Cone

6. The volume of a Prism:

V = b × h

Where,

V	Volume of Prism
b	Area of Base of Prism
h	Height of Prism

Solved Examples

Q. The dimensions of a rectangular water tank are given as 2m 75cm, 1m 80cm, and 1m 40cm. How many liters of water can be filled in the tank?

Solution:

As we know that 1m=100cm

Dimensions of the tank are 2m 75cm and 1m 80cm and 1m 40cm.

These can be written as 275cm, 180 cm, 140 cm

Now, we know that the volume of the cuboid is,

V= l × b × h

V = 275 × 180 × 140

V = 6930000cm³

Since 1000 cm³= 1 Liter

Thus, V=6930 liters

Hence the tank will hold 6930 liters of water.

Q. How many persons can be accommodated in a big room of length 16m, breadth 12.5m, and height 4.5m. Assume that 3.6 m³ of air is needed for each person?

Solution:

First, we will compute the volume of the room of cuboid shape:

V = l × b × h

= 16 × 12.5 × 4.5

= 900 m³

Also, it is given that 3.6 m³ of air is needed for each person.

So, the total number of persons can be accommodated in the room is:

Total volume/ volume required by each person

= \(\frac{900}{3.6}\)

= 250 people.