Help with Calculus: Maximising Volume of Hot Metal Storage Tank

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Homework Help Overview

The discussion revolves around a calculus problem involving the maximization of the volume of a hot metal storage tank, which has a rectangular shape with a square cross-section. The problem requires participants to explore the relationship between the surface area and volume of the tank, specifically how to express volume in terms of surface area and find conditions for maximizing volume.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to eliminate a variable (n) between the equations for surface area and volume. There are inquiries about the steps involved in deriving the maximum volume condition and the implications of setting the derivative of volume with respect to x to zero.

Discussion Status

The conversation indicates that some participants are seeking clarification on the steps to take, while others emphasize the importance of showing attempts at the problem to facilitate guidance. There is a recognition of the need to work through the equations rather than simply receiving a solution.

Contextual Notes

Participants express uncertainty about how to approach the problem, indicating that it is a new type of question for them. There is a mention of imposed rules on the forum that discourage providing complete solutions without prior attempts from the original poster.

hiya99
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help Calculus!

Homework Statement



got this question, and i need help. lost it lol. this is the sort of question i have to do for me assignment. Help in going through it

Homework Equations



Hot metal storage tank: is rectangle with a square cross section
total surface area is: A=xSquared(4n+2) The Volume is:V=nxcubed
Too maximise effeciency by minimising heat loss through the surface, the tank needs to be designed for a maximum volume for any given surface area.

by eliminating (n) between the two equations, show that for this shape, the volume is maximum (dV/dx=0) when the total surface area A is 6x. Calculate the value of n for this maximum volume and hence calculate the maximum voume of the tank with a total surface area of 24m

i have the question on sheet if u would like to read it properly cheers for any help

The Attempt at a Solution

 
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What have you done so far? What have you tried? The general rule on this forum is that you show what you have attempted so that people can tell you where you have gone wrong, or can help you with the next step.
 


sorry just trying to find someone who can help go through the steps of this question as it a bit new to me any help is great
 


If someone could show me steps in this question woul be very grateful
 


The steps are given, but I'll try to clarify them.

Solve the equation for surface area for n, and plug that value into the equation for volume. Now take the derivative of this new equation for volume with respect to x and set it equal to zero and solve it for A. Take the calculated value for A and use it to find n. Once you know n, you can then find x by using the given surface area. Finally use the calculated values of n and x to find V.
 
Last edited:


thanks i plug these into my equation but get lost. this is an example question i will get for my coursework. i understand in puttin gin the number but wanted someone to show me how to work this out. thank you
 


hiya99 said:
If someone could show me steps in this question woul be very grateful

As it said in the problem statement, start by eliminating n from the two equations. What do you get when you do that?

p.s. By the rules of Physics Forums, nobody at this forum is just going to do the problem for you. You'll need to make an attempt at the solution.
 

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