I made a cylinder in paper. I cut a cone with one side the cylinder base and tip of cone from center point of other side of cylinder (Like a Triangle). Once it is cut, other two cones that are formed from the left out area is not same size as that of the cut one.
But, volume of cone is 1/3 of the volume of cylinder (But three cones of same size and volume is not formed).
Correct if im wrong.
Your question is not so clear: I presume you want to know if the lateral surface of a cylinder (of base radius $r$ and height $h$) is less then three times the lateral surface of a cone with the same base and height. $$ \text{lateral surface of cylinder:}\quad A_{cyl}=2\pi rh; $$ $$ \text{lateral surface of cone:}\quad A_{cone}=\pi r\sqrt{r^2+h^2}. $$ Hence: $$ {A_{cyl}\over A_{cone}}={2\over\sqrt{1+(r/h)^2}} $$ and this quantity is always less than $2$. For $r/h>3$ it is less than $1$: in that case you won't be able to cut out even a single cone from the cylinder.