Listly by James Johnson
Interesting facts which nobody knows about volume of a sphere
Defined as a perfectly round geometrical object, residing in a three dimensional space. It is much like the surface of a ball, like basketball etc.
The only difference between a circle and a sphere is that a circle is in a two dimensional Space. It is mathematically described as the bunch of points converging from a specific point with the same distance. Trapezoid area calculator can be very important for your learning & practice.
The volume enclosed within this ball like object is expressed as:
V = 4/3лr3
If we put the value of л= 3.14 and solve for V, then V= 4.19r3 since, 4, 3 and pi are constant.
The concept of spheres was introduced by Archimedes, a great mathematician. He used to be amazed by curves, inside his creative mind, he started constructing lines that were shaped in both dimensions; 2d and 3d.
He was in search of something more intellectual and challenging at the same time, eventually, he built up circles, parabolas and spheres.
His passion made him the first person to compute and express the formulas for the volume of a sphere. How did he manage to do that?
The surface of a sphere is hard to get a grip on, because it changes at each point. Archimedes, assumed cutting a ball into two equal halves. Each half called as a hemisphere. Now, it was easy to work with a hemisphere having a flat surface.
He then pictured, putting the half ball’s face down on a flat surface. Next, he imagined and fixed a cylindrical object around the hemisphere.
The circular area built at the top of the cylindrical object was of the same measurement as that of the bottom end. Moreover the height of both the cylinder and hemisphere was also the same as illustrated below:
He then imagined cutting horizontal pieces or slices through the cylindrical object, with each slice an inner circle increased in size. With cutting a little down the cylinder, the cross sectional area continued to expand. At the final slice, the blue hemisphere ring vanished and its area was zero.
He then combined all the sliced areas, stacking them altogether, he multiplied the depth of the blue areas with their number to find the volume.
Archimedes concluded that the volumes of the blue areas summed up to the space occupied by a cone, having the same base and height as that of the cylinder.
According to this statement, the volume of the hemisphere was equal to the volume of the cylinder minus that of the cone.
This gave him the volume of hemisphere= 2/3πr3
We know that hemisphere is half of sphere, so the formula = 4/3 πr3
A general fact about all spherical objects is that they have the largest volume for a small fixed surface area. Example; a balloon, when filled with air containing the large volume of air for the fixed surface area.
When we look around, we will find the smallest possible examples of spheres in nature like; bubbles, dew drops etc. On the other hand some gigantic examples like planets.
Let’s not go too far, the planet inhabited by us, the earth is itself a spheroid, after many years of discussions, it is now an established fact that the earth is nearly a sphere, but not completely because it is squashed at the poles.
In the end, I hope this article will prove beneficial and you will learn a lot about these fascinating geometrical objects, if you are interested in calculation of the volume of spheres with ease, volume of a sphere calculator.
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We are all familiar with a sphere, which is a completely round object in geometry. If you are a student fascinated with geometrical objects like a sphere, you will find this article quite interesting.
In this article, we will define the sphere and its volume, look behind in the past and study its origin and finally discuss some of the interesting facts. Now, let’s get started;