Question 179127
that is a pretty complicated question:
:
the derivation of the Volume of a sphere involves Calculus.
:
The answer is not easy to illustrate. here is a partial explanation
:
Let's start with the surface area.  Take a sphere of radius R, and 
imagine constructing a cylindrical box with radius R and height 2R.  
You can see that the sphere will fit snugly inside this box.

Archimedes, the Greek mathematician, proved a surprising fact: the 
surface area of the sphere is exactly the same as the lateral surface 
area of the cylinder (that is, the surface area not including the two 
circular ends).  You can calculate the lateral surface area of the 
cylinder and you will see that it is 4*pi*R^2.  The following item in 
the Dr. Math Archives describes what Archimedes did to prove this 
result:

  In brief, you can imagine drawing a tiny triangle on 
the surface of the sphere and connecting its corners to the center of 
the sphere.  You have made a very narrow pyramid.  The volume of a 
pyramid is 1/3 times the area of the base times the height.  Thus the 
volume of this pyramid is 1/3 times the radius of the sphere, times 
the area of that little triangle.

Now, imagine that you cover the sphere with tiny triangles, and thus 
cut the sphere into millions of narrow pyramids.  The total volume of 
the pyramids is 1/3 times the radius of the sphere times the sum of 
the areas of the tiny triangles.  In other words, the volume of the 
sphere is 1/3 times R times the surface area of the sphere!

  V = (1/3)R * 4*pi*R^2
    = (4/3)pi*R^3