Many friends or classmates don't understand integral. So I can make a simple explanation with reasonable logic, which can be understood by junior high school and senior high school mathematics. As follows:

First, give a cylinder with a height of h and a bottom radius of r (h and r are not infinite).

Then, make a cylinder according to the bottom and height.

How to compare two volumes? The critical moment has arrived.

Here are some definitions first.

1, assuming that God exists;

2. Cut evenly parallel to the bottom of the cylinder for n times with a magic knife, so that n is infinite, and (N+ 1) sections of the cylinder and the cone are obtained, and the section thickness is h/(n+1);

3. Infinite tangent, making n infinite to a certain extent, and getting Δ r = r/n, so Δ r is the radius of the cone (not smaller, similar to electron charge). This is the key to logic, please understand deeply.

By understanding the above definition, we can know the relevant calculation data. For all parts of the cone,

The radius of each segment is 0, δ r, 2 δ r, … m δ r, … n δ r = r from top to bottom (because δ r has been defined as inseparable).

The area of each section of the cone is 0, π δ r 2, π (2δ r) 2...π (nδ r) 2 from top to bottom,

The volume of each single section is the cross-sectional area *(H/(N+ 1)).

So the volume of the cone is equal to the sum of the volumes of all sections.

V cone = (π δ r 2) * (0+ 1+2 2+3 2+...+n 2) * (h/(n+ 1))

Let's look at the volume of the cylinder again. It is the sum of (N+ 1) cylindrical cross-sectional volumes, which is very simple.

V column = (n+1) * (π R2) * (h/(n+1)) = (n+1) * (π (nδ r) 2) * (h/(n+65438+))

Therefore, V cone /V column = (0+1+2 2+3 2+...+n 2)/((n 2) * (n+1)).

According to the knowledge of the sequence,

V cone /V column = n * (n+1) * (2n+1)/6/((n 2) * (n+1)) =1(6n.

Therefore, when n is infinite, V cone /V column = 1/3.