Volume can be explained as “how much space does this take up” or “how much water do we need to fill this thing up.” Obviously a good starting reference point for my question here is both the cube and the rectangular prism, whose volume formula is simply length*width*height. Once we get to stuff like cones, pyramids, spheres, and cylinders, formulas start throwing people in for a loop, giving you various hoops that you have to go through. Don’t even get me started on inner tubes ([https://en.wikipedia.org/wiki/Solid_torus](https://en.wikipedia.org/wiki/Solid_torus) ) and vases ([https://en.wikipedia.org/wiki/Solid_of_revolution](https://en.wikipedia.org/wiki/Solid_of_revolution) ). In any case, how did we manage to create formulas for the volumes of solids that aren’t boxes?
In: Mathematics
With the use of calculus, by taking the integral of the shape but where numbers like height and width have been substituted with variables.
For example, if you take a right triangle where one side is on the x-axis and rotate it around an axis of the graph, you get a cone. You can use integration to find the volume of this shape. If you put variables in where the height and width of the triangle should go and solve this integral then your answer to that integral will be a general purpose solution for the volume of a cone.
https://brilliant.org/wiki/volume-cone/ here is this concept visualized.
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