Question

This is a rather silly question haha
is there proofs to volumes of some solids without knowing the integral. Just basic geometry intuition
I believe ancient mathematicians derived many volumes and areas of known solids and planes without calculus.

Answer 1

@ganeshie8

Answer 2

@ash2326

Answer 3

@robtobey

Answer 4

@ikram002p @Kainui @dan815

Answer 5

I've been asking myself this one for a long time

Answer 6

me too :3 i remember pondering on this topic a couple of years ago... there is a general formula known to ancient mathematicians for finding the volume of solid of ANY shape bounded between two planes... but i don't seem to recall the name of that formula...
its not steinmetz solid formula but its closely related to this shape
http://mathworld.wolfram.com/SteinmetzSolid.html

Answer 7

I got your point, I believe too that it is the bounding concept to approach any shape's volume.

Answer 8

its not archimedes approximation, its more involved than that
il post the link once i find it..

Answer 9

Let's take a sphere for example, what type of shapes that we can use to bound it

Answer 10

Archimedes approach doesn't work for every solids and shape
what if the shape is floating, we can know it's volume.

Answer 11

can't*

Answer 12

interesting, how does archimeded approach work ? xD

Answer 13

let's say you got a heavy random shape, and we got a volume of water. the make things easy we use the cubic shape that has measurements instruction. we fill it with some water
but not fully, then we put that shape inside. the level of water will rise up. Archimedes concluded that the level of water that was added is the volume of the shape we put in the water. Archimedes realized this when he was swimming and saw that the water rose up.

Answer 14

gotcha :) the way we find volumes in chemistry lab !

Answer 15

Yeah that's Archimedes experiment!

Answer 16

But he studied many shapes and did a lot of experiments. He wouldn't the actual formula of some volume just by that. he needed to compare his results with other known shapes
and therefore make conclusions

Answer 17

He wouldn't get*

Answer 18

@SolomonZelman

Answer 19

Waiting for more ideas! I'm considering to re study geometry with the intent to see through
questions that are kept unanswered to me

Answer 20

@zepdrix

Answer 21

@thomaster

Answer 22

mmm what i know that they counted on this idea :-
volume=base area * height
when both bases are the same
like this


how ever othere shapes they used experiment like water volume to count
like how cone volume related to cilendrical mmm
as i know there is no general formulla used for all , i mean each volume had its special story how did they find it :P