The **volume of sphere** is the capacity it has. The shape of the sphere is round and three -dimensional. It has three axes such as x-axis, y-axis and z-axis which defines its shape. All the things like football and basketball are examples of the sphere which have volume. The volume here depends on the diameter of radius of the sphere, since if we take the cross-section of the sphere, it is a circle. The surface area of sphere is the area or region of its outer surface. To calculate the sphere volume, whose radius is ‘r’ we have the below formula:

Volume of a sphere = 4/3 πr^{3} |

Now let us learn here to derive this formula and also solve some questions with us to master the concept.

If you consider a circle and a sphere, both are round. The circle can be drawn on a piece of paper but the sphere cannot be drawn on the paper. The difference between the two shapes is that a circle is a two-dimensional shape and sphere is a three-dimensional shape which is the reason that we can measure Volume and area of a Sphere.

**Sphere Volume**

The sphere is defined as the **three-dimensional round solid figure** in which every point on its surface is equidistant from its centre. The fixed distance is called the radius of the sphere and the fixed point is called the centre of the sphere. When the circle is rotated, we will observe the change of shape. Thus, the three-dimensional shape sphere is obtained from the rotation of the two-dimensional object called a circle

Archimedes principle helps us to find the volume of a spherical object. It states that when a solid object is engaged in a container filled with water, the volume of the solid object can be obtained. Because the volume of water that flows from the container is equal to the volume of the spherical object.

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## Volume of Sphere Formula

To find the formula for a sphere, let’s study Archimedes Principal first.According to the Archimedes Principle, the spherical object is placed inside a solid container in which the radius of the spherical object is equal to the radius of the circular bases of the cylinder. And also, the spherical object meets the top and bottom of the cylindrical container, the diameter of the spherical object is equal to the height of the cylindrical container.

Let, the volume of the spherical object is assumed to be **⅔** rd of the cylindrical container.

The Volume of sphere = 2/3 of the volume of the cylinder …….. (1)

It is observed from the above figure, h = d = 2r

We know that the volume of a cylinder = πr^{2}h cubic units. ……(2)

Substitute (2) in (1), we get

The volume of sphere = (2/3) πr^{2}h …..( 3)

Now, substitute the value of “h” in (3),

The volume of sphere = (2/3) πr^{2} (2r)

It becomes, V = 4/3 πr^{3}

Therefore, **The volume of a sphere= 4/3 πr ^{3}**

**Cubic units.**

**Surface Area of Sphere = 4 πr ^{2}**

You can easily find the volume of the sphere and equation of sphere if you have the measurements of the radius

### Examples

**Q.1: Find the volume of a sphere whose radius is 3 cm?**

### Solution :

### Given: Radius, r = cm

Volume of a sphere = 4/3 πr** ^{3}** cubic units

V = 4/3 x 3.14 x 3^{3}

V = 4/3 x 3.14 x 3 x 3 x 3

V = 113.04 cm^{3}

**Q.2: Find the volume of sphere whose diameter is 10cm.**

Solution: Given, diameter = 10cm

So, radius = diameter/2 = 10/2 = 5cm

As per the formula of sphere volume, we know;

Volume = 4/3 πr** ^{3}** cubic units

V = 4/3 π 5^{3}

V = 4/3 x 22/7 x 5 x 5 x 5

V = 4/3 x 22/7 x 125

V = 523.8 cu.cm.

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## Frequently Asked Questions on Volume of Sphere

### What is the formula for volume of sphere?

The formula to calculate the volume of sphere is defined by: 4/3rd of Pi and cube of radius of sphere.

### How to calculate volume of a sphere?

To find the volume of sphere we have to use the formula:

Volume = 4/3 π r^3

Where ‘r‘ is the radius of the sphere.

### What is the total surface area of the sphere?

The total surface area of any given sphere is equal to;

A = 4πr^2

Where ‘r’ is the radius of the given sphere.

### What is the ratio of volume of sphere and volume of cylinder?

The volume of any sphere is 2/3rd of the volume of any cylinder with equivalent radius and height equal to the diameter.