Please help find volume:
If 1400 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Question

turingtest · Answer

We need two equations here, one for surface area (which has a restriction of 1400 sq cm) and one for volume (which we need to maximize) can you write the equations? (I'm eating right now... :/)

anonymous · Answer

i think I do I was trying to do just volume and thats how i got lost, would you mind just one more. i know I have to do pythagoream (bad spelling) theory but the find what to plug is confusing the question is; A fence 6 feet tall runs parallel to a tall building at a distance of 2 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

anonymous · Answer

I'm sorry to bombard you with the question i just have an exam in about half an hour and I want to make sure i know how to set up

turingtest · Answer

ok, one thing at a time:

what is the general formula for the area of a rectangle?
how many rectangles make up our box?
what are the dimensions of these rectangles?
what is the total surface area of the box?

Try to write the formula for the surface area of this box, that is the first step.

turingtest · Answer

I'll help you, let one side of our SQUARE base be x, and the height be h. there is no top to the box so we have 
1 square base
4 rectangular sides
So what is the formula for our total surface area of the box?

If you cannot answer that I'm afraid cramming for your test right now will not likely help you.

anonymous · Answer

s.a is 2ab + 2bc + 2ac so would it be 4 times one side and then the other side?

anonymous · Answer

thank you i really do appreciate the help I have to run though, you're explanation was great I just have to read the problem well because I do have a good idea of where the numbers would then go. have a great day and thank you again, if you leave anything else ill make sure to read the notes when i get back on

turingtest · Answer

that formula would be true for a box with length=a height=b depth=c
but our problem is easier. Why? because we have a square base. so if one so is of our base is s our base is x, the area of the base is x^2
What about the area of the sides if the height is h?

Here is what it is, figure out why later I guess
$$A=x^2+4xh=1400$$$$V=x^2h$$

turingtest · Answer

so if one side of our base is x*