SOLUTION: This is a calculus problem. A cylindrical container is to hold 20π cm3. The bottom is made of a material that costs $0.80 per cm2, and the top is left open (no material needed
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Question 858725: This is a calculus problem. A cylindrical container is to hold 20π cm3. The bottom is made of a material that costs $0.80 per cm2, and the top is left open (no material needed). The material for the curved side costs $0.32 per cm2.
Find the height in centimeters of the most economical container.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Find the volume of a cylinder,
Find the total cost by calculating the area of the bottom and area of the side wall and multiplying by cost per unit area.
From the volume equation, you can find a relationship between H and R.
Substitute,
Now you have total cost T as a function of one variable.
Take the derivative and set it to zero.
Then,
.
.
.
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