I have a problem how to start this question.....A right cylinder si to be madde so that the sum of it radius and height is 9cm. Find the maximum volume of the cylinder.
Hello, Aalrin!
A right cylinder si to be madde so that the sum of it radius and height is 9 cm.
Find the maximum volume of the cylinder.
The volume of a cylinder is: .$\displaystyle V \:=\:\pi r^2h$ [1]
We are told: .$\displaystyle r + h \:=\:9\quad\Rightarrow\quad h = 9 - r$ [2]
Substitute [2] into [1]: .$\displaystyle V \:=\:\pi r^2(9 - r)$
Hence, we must maximize: .$\displaystyle V \:=\:\pi(9r^2 - r^3)$
Can you finish it now?