SOLUTION: A rectangular box with a square base and open top is to be made. Find the volume of the largest box that can be made from 432 sq. m. of material.

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Question 1119872: A rectangular box with a square base and open top is to be made. Find the volume of the largest box that can be made from 432 sq. m. of material.
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39629)   (Show Source):
You can put this solution on YOUR website!
x by x base
y height
v, the volume

Substitute for y in v, simplify, and look for the minimum point of v.

Answer by ikleyn(52873)   (Show Source):
You can put this solution on YOUR website!
.
In a way on how this post is worded and presented, it is not a Math problem at all.

So, it does not deserve any serious consideration.

To become a Math problem, it needs to be totally re-formulated.

I know how to do it, but I think it is not my job and function to formulate it for / (instead of) you.

In opposite, it is YOUR DUTY to bring clear and correct formulation.

Answer by greenestamps(13208)   (Show Source):
You can put this solution on YOUR website!

Let the side of the square base be x and the height be h. Then

(1) the total surface area (base and 4 sides) in square meters is 432:

(2) the volume (to be maximized) is the area of the base times the height:

Solve equation (1) for h and substitute in equation (2) to get an expression for the volume in terms of the single variable x:

Take the derivative and set it equal to 0 to find the value of x that maximizes the volume; and calculate the volume for that value of x:

The maximum volume is 864 cubic meters, when the square base is 12m on a side and the height is 6m.