Volume of Pyramid/Cone

Thanks for coming on the blog. Yesterday I was trying to figure out the volume of a sphere without the use of calculus. I observed many things which I would not like to share right now cos its too long. The really interesting thing I observed were the pyramids. to be honest They weren't pyramid but a shape you would get around the corners if you if you put a sphere in a cube (my actual method didnt use cubes but used cylinders for finding the v sphere. only have i used cubes for the v cone).
Here's how I derived the same formula for volume of a pyramid, which is lbh/3. A cube can be cut into 6 pieces of equal volume V from the centre. Here's a image I got from google images. Also V = 1/6 A^3 where A is the side length of the cube

Now the slant part of a pyramid is straight also it can be reasoned that the volume of a pyramid is dependent upon A^2 (base area) and A (height) which means that 

V = 1/6*A^2*A

V = 1/6*A^2*2H since A = 2H

V = 1/3*A^2*H

V = 1/3*L*B*H

We can extend the same method to cones. We know that volume is dependant upon the base area and a cone the base area is merely pi*r^2

V cone = 1/3*pi*r^2*h

I will try to somehow extend this to spheres and see if there's a way to find the volume of a sphere without the use of calculus. And one more thing, my exams are finally over and my 12 days holiday has begun. I really dont like school and feel really great to get a leave. So that would be all for today. Thank you very much for reading. Hope you have a great day.