Asked by Megan
You are in charge of a tank to be used for water storage. Your boss has told you that he wants a cylindrical tank with a minimum capacity of 300,000 cubic feet. Your boss wants to spend the least possible amount in painting the tank. Design a tank to meet this objective.
Answers
Answered by
drwls
Let y be the height. The diameter D must satisfy
(pi/4) D^2 y = 3*10^5 ft^3
The area to be painted (including the top) is
A = pi [D^2/4 + D y]
Substitute using the first equation to eliminate y.
A = pi [D^2/4 + 3*10^5 (4/pi)(1/D)]
Set dA/dD = 0 and solve for D
D/2 - (12*10^5/pi)/D^2 = 0
D^3 = 24*10^5/pi
D = 92.6 ft
(pi/4) D^2 y = 3*10^5 ft^3
The area to be painted (including the top) is
A = pi [D^2/4 + D y]
Substitute using the first equation to eliminate y.
A = pi [D^2/4 + 3*10^5 (4/pi)(1/D)]
Set dA/dD = 0 and solve for D
D/2 - (12*10^5/pi)/D^2 = 0
D^3 = 24*10^5/pi
D = 92.6 ft
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.