SOLUTION: A cylinder has a volume of 20 pi inches ^3. The base and top are made of aluminium that costs $4 per sq inch. The sides are made from rolled steel at a cost of $3.2 per sq inch.
Algebra ->
Volume
-> SOLUTION: A cylinder has a volume of 20 pi inches ^3. The base and top are made of aluminium that costs $4 per sq inch. The sides are made from rolled steel at a cost of $3.2 per sq inch.
Log On
Question 798403: A cylinder has a volume of 20 pi inches ^3. The base and top are made of aluminium that costs $4 per sq inch. The sides are made from rolled steel at a cost of $3.2 per sq inch.
What is the height of the cheapest container?
So far: V = pi r^2 h therefore 20pi=pi r^2 h...... therefore h = 20pi/pi r^2
h=20/r^2
Cost= (lid cost)+(base cost)+(side cost)
Therefore Cost = 4(pi r^2) + 4(pi r^2) + 3.2(2pi r h)
= 4(pi r^2) + 4(pi r^2) + 3.2(2pi r)(20/r^2) subs h
= 8(pi r^2) + 128pi/r
C' therefore = 16pi r - 128pi/r^2
now I'm stuck, I feel I should multiply top and bottom by r^2 but I cannot see why Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! You seem to be going in the right direction.
I'll push you the last fraction of an inch.
For minimum cost, you want C'=0, which means --> --> --> {{r^3=128/16}}} --> -->
So
