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 πr3|
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.
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.
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 = πr2h cubic units. ……(2)
Substitute (2) in (1), we get
The volume of sphere = (2/3) πr2h …..( 3)
Now, substitute the value of “h” in (3),
The volume of sphere = (2/3) πr2 (2r)
It becomes, V = 4/3 πr3
Therefore, The volume of a sphere= 4/3 πr3 Cubic units.
Surface Area of Sphere = 4 πr2
You can easily find the volume of the sphere and equation of sphere if you have the measurements of the radius
Q.1: Find the volume of a sphere whose radius is 3 cm?
Given: Radius, r = cm
Volume of a sphere = 4/3 πr3 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 cm3
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 πr3 cubic units
V = 4/3 π 53
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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