anonymous
  • anonymous
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
chestercat
  • chestercat
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tkhunny
  • tkhunny
Can you describe the total surface area?
anonymous
  • anonymous
im not sure
tkhunny
  • 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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anonymous
  • anonymous
v= x^2 *y
anonymous
  • anonymous
which will be y= 4/x^2
anonymous
  • anonymous
am I right?
tkhunny
  • 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
  • anonymous
I dont know how to find the surface area
tkhunny
  • 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
  • anonymous
A= 2xy+2xy+2x^2 ?
anonymous
  • anonymous
A=x^2+2xy+2xy
anonymous
  • anonymous
A=X^2 + 16/x ?
tkhunny
  • 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
  • anonymous
take the derivative
tkhunny
  • tkhunny
That's it. What do you get?
anonymous
  • anonymous
2x -16/x^2
tkhunny
  • tkhunny
Perfect. Next?
anonymous
  • anonymous
find the domain ?>
anonymous
  • anonymous
0 to infinity ?
anonymous
  • anonymous
then make it equal to 0
anonymous
  • anonymous
i got x=2
tkhunny
  • 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
  • tkhunny
Yes, x = 2 is the only Real Solution.
tkhunny
  • tkhunny
Now, and finally, answer the original question. At this point, most folks have forgotten what the question was!
anonymous
  • anonymous
box measures 2m*2m height of he box is 1m
anonymous
  • anonymous
thank you
tkhunny
  • tkhunny
You did well. Excellent work!

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