Volume of a Sphere - The volume of a sphere is equal to 4⁄3 times Pi (π) times the radius cubed.
For example, if a sphere has radius 3, then the volume of that sphere is,
V = 4/3 πr3 = 4/3 x 3.14 x 33 = 4/3 x 3.14 x 3 x 3 x 3 = 113.04 cm3
Sphere - Perfect round shape in 3-dimensional space
A sphere is a perfectly round geometrical shape in 3-D space. It is also defined as a set of all points placed at distance r (radius) away from a fixed center. It is quite symmetrical and has no edges or corners. Sphere has 3 axes like the x-axis, y-axis, and z-axis. Some well-known examples of Sphere are like football or basketball.
The Volume of a Sphere
The volume of the sphere is the actual capacity of the sphere. The volume of a sphere based on the diameter of the radius of the sphere as we can consider the cross-section of the sphere as a circle. The volume of a Sphere can calculate using a Volume of a Sphere calculator easily, you just need the radius of the sphere.
The volume of a sphere is four-thirds times pi times the radius cubed if we consider formula then,
Volume, V = 4/3 πr3
What is the Formula for Finding the Volume of a Sphere?
This handy Volume of a Sphere Calculator is very useful to find the volume of a sphere by just entering the radius of the sphere but what if you want to find out using formula? Let's discuss more on it and learn it easily.
The sphere is described as the 3-D round solid shape and in this shape, every point on its boundary is at the fixed distance from its middle point. This fixed distance is termed as the radius of the sphere and the middle point is named as the center of the sphere.
To derive the formula for the volume of a sphere, we can consider the Archimedes principle. As he stated that when a solid object is used as a container and loaded with water, the volume of the solid object can be determined. As the volume of water that filled in the container is the same as the volume of the spherical shape.
Also as per the Archimedes Principle, the spherical shape is put into a solid container in which the radius of the spherical object and the solid container are the same. And further, the spherical object has the same sized top and bottom as the cylindrical container has. And the diameter of the spherical shape is the same as the height of the cylindrical container.
Now to derive the formula, let assume that the volume of the spherical shape is ⅔ rd of the cylindrical container.
So the volume of the sphere is equal to the 2/3 of the volume of the cylinder
It is proved that the diameter (height) of an object is the same as the twice radius, means, d = 2r
Now, we know the volume of a cylinder = πr2h cubic units
As we see above, Volume of sphere = 2/3 of the volume of the cylinder
So, the volume of sphere = (2/3) πr2h
Now, if we consider h = 2r here
Volume of sphere = (2/3) πr2 (2r) = 4/3 πr3
Hence, Formula of the volume of a sphere is,
Volume, V = 4/3 πr3 Cubic units.
Step by Step Calculation of the Volume of a Sphere
Now if you have been asked to find out the volume of a sphere, then just go through below easy steps one by one:
Step 1:From the given data, find out the radius of the sphere.
Step 2:Now we know the value of pie is 3.14 so just do the multiplication of 4, 3.14 and cube of the radius (or 3-time radius)
Step 3: Divide the answer of this multiplication by 3 and note down the answer with Cubic unit.
Let's learn it using some examples!
Example 1: Find the volume of a sphere with a 6 cm radius?
Volume of a sphere = 4/3 πr3 cubic units
V = 4/3 x 3.14 x 63
V = 4/3 x 3.14 x 6 X 6 X 6
V = 904.32 cm3
Example 2: Find the volume of a sphere with a diameter of 8 cm.
Here, from given data, we have diameter of 8 cm
so, radius = diameter/2 = 8 / 2 = 4 cm
Now the formula of sphere volume,
Volume, V = 4/3 πr3 cubic units
V = 4/3 π 43
V = 4/3 x 3.14 x 4 x 4 x 4
V = 4/3 x 3.14 x 64
V = 268 cu.cm.
Example 3:The Volume of a sphere is 33.51 cm3, find the radius of it.
V = 4/3 π r3
33.51 = 4/3 x 3.14 x r3
33.51 = 4/3 x 3.14 x r3
r3 = (33.51 X 3) / (4 X 3.14)
r3 = 8
r = 2
So the radius of the sphere is 2 cm.