What is a Sphere? 

 

A sphere is a set of all points in a 3-dimensional space lying equidistant from the center. A sphere is a round, ball-like figure which has no faces, vertices, or edges but a continuous surface. Let's move on to learn how to calculate the volume of a sphere but before that look at the definition of the sphere. In a sphere, all the points on the surface are at equal distance from the center at any axes (X, Y, Z).

 

Sphere definition

 

A sphere is a set of points in space equidistant from a fixed point. This fixed point is the centre of the sphere.

 

Real Life Examples of a Sphere

 

1. Orange
2. Football
3. Globe
4. Planets
5. Sun
6. Moon. 

 

Properties of a Sphere

 

1. Perfect Symmetry: A sphere is perfectly symmetrical
2. All the points on a surface of a sphere are at equal distance (r) from the centre. 
3. A sphere has no vertices, no faces, no edges. 
4. Diameter of Sphere: The diameter of the sphere is the longest straight line segment that connects two points of the sphere and passes through the centre. The diameter of the sphere is two times the radius. 
5. The sphere possesses constant width and constant girth. 
6. A sphere which is a 3 dimensional round geometrical figure has the smallest surface area but the greatest volume. 

 

Difference between a Circle and a Sphere?

 

Let us learn the major differences between a circle and a sphere. 

 

 

Differentiating Property	Circle	Sphere
Dimension	2D	3D
Area Formula	Area of Circle=?r2	Sphere Surface Area=4?r2
Diameter Formula	Circle Diameter = 2r	Sphere Diameter = 2r
Circumference Formula	Circumference of circle = 2?r	No Circumference
Volume Formula	No Volume	Volume of Sphere= 4/3?r3

Difference between Circle and a Sphere

 

What is the volume of a sphere?

 

Volume is a measure of how much space is occupied by a solid object. Volume of a sphere is the notation of how much capacity it has. 

 

Volume of a Sphere Formula:

 

Now, let us see how to measure the volume of a sphere. 

 

The volume of a sphere is equal to 4/3 ? times the cube of its radius. This gives us the idea that Volume of a Sphere = 4/3 ?r3 where r is the radius of the sphere.

 

Since a hemisphere is half of a sphere, can you guess what the volume of a hemisphere will be? Yes, it is � of 4/3 ?r3 = ? ?r3.  

 

So, Volume of a Hemisphere = ? ?r3 where r is the radius of the hemisphere.

 

Now let us take some examples. 

 

1. Find the volume of a sphere of radius 11.2 cm.

 

Solution : Required volume = 4/3 ?r3

 

?4/3 x 22/7 x 11.2 x11.2 x11.2cm3 = 5887.32 cm cube.

 

2. A shot-putt is a metallic sphere of radius 4.9 cm. If the density of the metal is 7.8 g per cm cube, find the mass of the shot-putt.

 

Solution: Since the shot-putt is a solid sphere made of metal and its mass is equal to the product of its volume and density, we need to find the volume of the sphere.

 

Now, volume of the sphere = 4/3?r3

 

? 4/3 x 22/7 x 4.9 x 4.9 x 4.9 cm cube

 

? 493 cm cube (nearly)

 

Further, the mass of 1 cm  cube of metal is 7.8 g.

 

Therefore, mass of the shot-putt = 7.8 � 493 g

 

? 3845.44 g = 3.85 kg (nearly)

 

3. A hemispherical bowl has a radius of 3.5 cm. What would be the volume of water it would contain?

 

Solution : The volume of water the bowl can contain = 2/3?r3

 

?2/3 x 22/7 x 3.5 x 3.5 x 3.5cm cube  = 89.8 cm cube.

 

Read More- Volume of a Cone: Definition, Formula, Properties, and Solved Examples