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.

- anonymous

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- tkhunny

Can you describe the total surface area?

- anonymous

im not sure

- tkhunny

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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## More answers

- anonymous

v= x^2 *y

- anonymous

which will be y= 4/x^2

- anonymous

am I right?

- tkhunny

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.

- anonymous

I dont know how to find the surface area

- tkhunny

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.

- anonymous

A= 2xy+2xy+2x^2 ?

- anonymous

A=x^2+2xy+2xy

- anonymous

A=X^2 + 16/x ?

- tkhunny

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?

- anonymous

take the derivative

- tkhunny

That's it. What do you get?

- anonymous

2x -16/x^2

- tkhunny

Perfect. Next?

- anonymous

find the domain ?>

- anonymous

0 to infinity ?

- anonymous

then make it equal to 0

- anonymous

i got x=2

- tkhunny

?? 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).

- tkhunny

Yes, x = 2 is the only Real Solution.

- tkhunny

Now, and finally, answer the original question. At this point, most folks have forgotten what the question was!

- anonymous

box measures 2m*2m height of he box is 1m

- anonymous

thank you

- tkhunny

You did well. Excellent work!

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