an open top box with a square base has volume V=4m^3. Find the dimensions of the box so that it uses the least amount of material.

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an open top box with a square base has volume V=4m^3. Find the dimensions of the box so that it uses the least amount of material.

Mathematics
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Can you describe the total surface area?
im not sure
What is the measure of one side of the square base? If it is not given in the problemn statement, just name it something so we can talk about it.

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v= x^2 *y
which will be y= 4/x^2
am I right?
Well, it's okay, but I personally find it a little unsatisfactory for one reason. You did not tell us what you were doing. had you done this first, i woudl ahve been delighted. x = measurement of the side of the base y = measurement of the height of the box. You have discussed the volume. Now you need to discuss the surface area. Remember that it does not have a lid.
I dont know how to find the surface area
Yes, you do. First, do we know WHY we need to talk about the surface area? Read the problem statement again and give me a clue.
A= 2xy+2xy+2x^2 ?
A=x^2+2xy+2xy
A=X^2 + 16/x ?
There you go again, just blurting out equations without describing what you are doing. :-) So, who was right about you knowing how to find the Surface Area? Good work! What's next?
take the derivative
That's it. What do you get?
2x -16/x^2
Perfect. Next?
find the domain ?>
0 to infinity ?
then make it equal to 0
i got x=2
?? I suppose. It's a REAL box, so x > 0. Infinity is probably not good. \(yx^{2} = 4\). It will be a very flat box if x > 5 or so. :et's just keep that in mind and find where that derivative is zero (0).
Yes, x = 2 is the only Real Solution.
Now, and finally, answer the original question. At this point, most folks have forgotten what the question was!
box measures 2m*2m height of he box is 1m
thank you
You did well. Excellent work!

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