SOLUTION: I was struggling with this question. Please help me dear tutor . find the height and the radius of a cylinder of volume 150cm^3 which has the least surface area .

Algebra ->  Volume -> SOLUTION: I was struggling with this question. Please help me dear tutor . find the height and the radius of a cylinder of volume 150cm^3 which has the least surface area .       Log On


   

Question 880814: I was struggling with this question. Please help me dear tutor . find the height and the radius of a cylinder of volume 150cm^3 which has the least surface area .
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the volume of the cylinder.
V=pi%2AR%5E2%2AL=150
Then first the surface area of the cylinder.
SA=2%2Api%2AR%5E2%2B2%2Api%2AR%2AL
Now substitute from the volume so that the surface area is now only a function of one variable.
L=150%2F%28piR%5E2%29
So then,
SA=2%2Api%2AR%5E2%2B2%2Api%2AR%2A%28150%2F%28piR%5E2%29%29
SA=2%2Api%2AR%5E2%2B300%2FR
To minimize the surface area, take the derivative with respect to R and set it equal to zero.
d%28SA%29%2FdR=4%2Api%2AR-300%2FR%5E2

R=%28175%2F%282%2Api%29%29%5E%281%2F3%29
So then you can work backwards to find L.