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.

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
RELATED QUESTIONS
Suppose you want to make a closed box with a square base. The material for the top and... (answered by Theo)

A can in the shape of a right circular cylinder is required to have a volume of 700 cubic (answered by nerdybill)

A cylinder has a volume of 4(pi) cm^3. If the radius and height are each tripled, what... (answered by Alan3354)

I have a problem setting up and solving word problems. Can someone please help me? Here... (answered by richwmiller)

Cost of a Can. A can in the shape of a right circular cylinder is required to have a... (answered by josgarithmetic)

An open-top, square bottom crate is made of two materials--the sides are made of a light... (answered by josgarithmetic)

A rectangular box with square base and a fixed volume (V) is to be made from two types of (answered by Fombitz)

A CYLINDER HAS A VOLUME OF 235.5 CUBIC INCHES. IF THE VALUE OF PI (3.14) USED TO... (answered by rapaljer)

how would you solve a problem such as: A rectangular piece of cardboard is made into an... (answered by scott8148)