Question

the formula for the volume of a cone is v=1/3pir^2h. The volume cone x is 2 times the volume of cone Y. Why the height of cone X is 2 times the heigh of the cone Y, and the radius of cone X is the same as the radius of cone Y.

Answer 1

I will try to explain with an example

Suppose you have the product (4x5x6) which would be 120

So if we double that we would get
2 x (4x5x6) or 240

Would we multiply the 2 by each of the factors of the original product ? Of course not.
We would multiply by only one of the factors so we could have
8x5x6 , or
4x10x6, or
4x5x12 to get our 240

The same thing applies to
(1/3)π r^2 h
if we double that result, we would multiply either the 1/3 or the π or the r^2 or the h by 2, but not all of them

so 2 (1/2)π r^2 h
can be written as (1/3)π r^2 (2h), that is,
I doubled the h and left everything else the same