Definition of the volume of a sphere

The volume of the sphere is defined as the capacity that a sphere has. In simple words, the space that the sphere occupies is called its volume. The volume of the sphere is generally measured in the form of cubic units namely in3, m3, cm3, and so on. A sphere is a three-dimensional figure and is round in shape. A sphere is a three-dimensional figure that means that it has three axes, z-axis, x-axis, and y-axis. These three axes normally define its shape. Different objects such as basketball and football are all examples of the sphere and so they gave specific volumes. 

What is meant by the sphere volume?

By the term volume of a sphere we mean the amount of space contained within a sphere. In mathematics, Sphere is considered a 3-D solid figure. The significance of a sphere is that every point on its surface lies at an equal distance from its centre. This fixed distance between the surface and its centre is considered the radius of the sphere. When the rotation of a circle takes place then we can observe a change in shape. This is known as a sphere. Hence it can be concluded that the 3-D shape of a sphere is obtained through rotating a 2-D object called the circle.

The formula for the volume of the sphere along with its derivation

The formula for calculating the volume of a sphere is given as Sphere volume = 4/3 r3 π (units)3.

The derivation for this formula has been provided below. A sphere’s volume can be easily obtained by utilising the method of integration. Let us consider that the volume of the sphere consists of several circular disks that are arranged one above another. The diameters of the disks one above another continuously vary Now if a disk is chosen with radius ‘r’ and thickness “dy” which is present at a distance of y away from the x-axis. Hence, the volume can be given as the circle’s area and the thickness of the product. Moreover, the circular disk’s radius can be expressed in the form of vertical dimension (y) by utilising Pythagoras theorem. Hence, the disc element’s volume, dV can be provided in the form of : 

dV = (r2 π) dy

dV = (R2 – y2) dy

Hence, overall volume of sphere is given by 

Now when the limit are substituted we get 

V = [(R3 – R3/3) + R3 – R3/3]

If the above process is simplified we get 

V = [2R3 – 2 R3/3] π

V = [6R3 – 2R3] π/3

V = π/3 (4R3)

Hence, the volume’s dimensional formula is given by V = 4/3 πR3 (Units)3

How can the volume of the sphere be calculated?

A sphere’s volume is the space enclosed within it. The volume of the sphere can be calculated by utilising the previous formula which has been derived. For computing the volume of a particular sphere the following steps can be followed.

• First, the radius of the given sphere must be identified. If the sphere’s diameter is previously known then it can be divided by 2 for obtaining the radius.

• Next, the radius’s cube that is r3 must be calculated. 

• After this, it should be multiplied by 4/3 and π.

• If this method is properly followed then the final answer can be easily obtained

Solved Examples

Q1. Find the volume of the sphere with a radius of 5cm? 

Solution: The provided radius is 5 cm. 

Hence, the volume of the sphere = π*4/3*r3 cubic units.

V = 3.14 * 4/3 * 53 = 523.33 cc

Q2. Find the volume of the sphere with diameter 8 cm

Solution: Given diameter = 8 cm.

Hence, the radius is diameter/2 = 8/2 = 4cm.

Thus, volume of sphere is π*4/3*r3 = 3.14 * 4/3 *43 = 267.95 cubic units.

MCQ

1. What is the value of π?

1. 3.12

2. 3.00

3. 3.14

4. 6.15

Answer (C) 3.14

2. What is the formula for the volume of the sphere?

1. π*4/3*r3

2. π*5/3*r3

3. π*4/3*r2

4. π*4/3*r3

Answer (D) π*4/3*r3

3. What is the 2-D figure for a sphere?

1. Square

2. Circle

3. Rectangle

4. Straight line

Answer (B) Circle

4. What is the volume of a sphere with a radius 3cm?

1. 113.04 cm3

2. 114 cm3

3. 112 cm3

4. 154 cm3

Answer A) 113.04 cm3

5. What is the volume of the sphere with a radius 10cm?

1. 4186.67 cm3

2. 514.1 cm3

3. 2114.23 cm3

4. 5477.21 cm3