Help with Calculus: Maximising Volume of Hot Metal Storage Tank

[hiya99]

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

 

[danago]

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.

 

[hiya99]

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

 

[hiya99]

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

 

[Random Variable]

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.

 

[hiya99]

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

 

[Redbelly98]

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.