Question

A cylinder has a volume of 432 cubic meters. What is the volume of a cylinder with dimensions one-third of the original?

Answer 1

Cylindervolume=hpir^2

V=432
432=hpir^2=original

if each is divided by 3 then
h turns to (1/3)h
r turns to (1/3)r
input  and find the effect

(1/3)hpi[(1/3)r]^2
(1/3)hpi(1/9)r^2
move 1/9 to front
(1/27)hpir^2
compared to original volume (which was hpir^2)

so therefor we multiply the original volume by 1/27

432*1/27=16

the new volume is 16 cubic meters

Answer 2

Finally with knew knowledge i have found a  more correct answer* 

so in order to find out 1/3 of our dimentions 
(since we size 1/3 on our height and radius) 
all we have to do is divide by 27
423 ÷ 27 = 16
our correct answer is 27 cubic meters³
:P