Question

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.

Answer 1

Can you describe the total surface area?

Answer 2

im not sure

Answer 3

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.

Answer 4

v= x^2 *y

Answer 5

which will be y= 4/x^2

Answer 6

am I right?

Answer 7

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.

Answer 8

I dont know how to find the surface area

Answer 9

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.

Answer 10

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

Answer 11

A=x^2+2xy+2xy

Answer 12

A=X^2 + 16/x ?

Answer 13

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?

Answer 14

take the derivative

Answer 15

That's it. What do you get?

Answer 16

2x -16/x^2

Answer 17

Perfect. Next?

Answer 18

find the domain ?>

Answer 19

0 to infinity ?

Answer 20

then make it equal to 0

Answer 21

i got x=2

Answer 22

?? 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).

Answer 23

Yes, x = 2 is the only Real Solution.

Answer 24

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

Answer 25

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

Answer 26

thank you

Answer 27

You did well. Excellent work!