How I divide a cone horizontally in three parts of same volume?

Answer 1

I shall do the first third.

The original cone has radius r₁ and height h₁

The volume is (1/3)π(r₁)²h₁

The cone "off off" to make the bottom 1/3 of the original has radius r₂ and hegith h₂.

The volume is (1/3)π(r₂)²h₂

The top part's volume is 2/3 that of the bottom truncated cone.

(1/3)π(r₂)²h = (2/3)(1/3)π(r₁)²h₁

Reducing

[(r₁)²h₁] / [(r₂)²h₂] = 2 / 3

The next third is has the ratio of 1 / 2.