Answer:
Possible dimensions are [tex]r=4\,\,cm\,,\,h=4\,\,cm[/tex] and [tex]h=16\,\,cm\,,\,r=2\,\,cm[/tex]
Step-by-step explanation:
Given:
Volume of a cylinder is [tex]64\pi\,\,cm^3[/tex]
To find: Dimensions of a cylinder
Solution:
Let [tex]r,h[/tex] denote height of a cylinder.
Volume of a cylinder = [tex]\pi r^2h[/tex]
Therefore,
[tex]64\pi=\pi r^2h\\64=r^2h\\4^2\,4=r^2h[/tex]
One possible dimension can be [tex]r=4\,\,cm\,,\,h=4\,\,cm[/tex].
Also, [tex]64=r^2h[/tex] can be written as [tex]16(2^2)=hr^2[/tex]
So, another possible dimension can be [tex]h=16\,\,cm\,,\,r=2\,\,cm[/tex]
