I managed to find the volume of a cone without calculus using an observation that I made.
First, I put a cone on a cartesian plane, with the tip at the origin. Thus, an equation to describe the radius(x) would be the radius over the height times x. Then, I substitued this equation into pi r squared to get cross sectional area as function of x.
I then observed how the volume of the cone could be approximated by using disks, the width of each being the height of the cone divided by the number of disks. So, the volume as a function of x would be the area as a function of x times the height divided by n, or the number of disks. However, instead of using integration to sum the volumes of all the disks, I observed that if I moved along the height in increments equal to the width of each cylinder, that the volumes of the cylinders increased in a sequence of squares, the second disk being 4 times the volume of the first, the third being 9 times, the fourth being 16 times, and so on.
To me, this showed that the second disk can be broken up into 4 cylinders equal to the volume of the first disk, the third into 9, the fourth into 16, and so on. So, the volume of a cone is equal to the volume of the first disk times the sum of all the cylinders, which we can get using the summation of squares formula. So, I got the volume of the first cylinder by putting the width of one cylinder into the volume as a function of x formula, which got pi r squared times the height over n cubed. I then multiplied this by the summation of squares formula to get
Then, I let n go to infinity, which resulted in the volume of a cone being (pi*r^2*h)/3.