You must have played or seen students playing games like football and basketball. All these things like football and basketball are examples of three-dimensional geometrical figures which we call “spheres”. 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.
What is the Sphere?
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.
How to Find the Volume of Sphere?
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.
You can easily find the volume of the sphere and equation of sphere if you have the measurements of the radius
Sample Problem
Question:
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 33
V = 4/3 x 3.14 x 3 x 3 x 3
V = 113.04 cm^{3}
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Volume of a Cylinder | Area Of a Circle |
Surface Area of a Cylinder | Surface Areas and Volume |