Question

A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. Let x denote the length of the side of the square being cut out. Let y denote the length of the base.

write the expression for the volume V:

write the volume as a function of x:

finish solving the problem by finding the largest volume the box can have:

Answer 1

I saw some answers online but I didn't understand their responses, I was wondering if someone could explain it to me a bit more clearly :)

Answer 2

I get that it would require an actual explanation but this is kind of the best I can do at the moment?

Answer 3

Okay, I will try, but it might take 5-10 minutes

Answer 4

okay thank you

Answer 5

Are you familiar with taking derivatives?

Answer 6

yup

Answer 7

I remember doing this last year when I was in calculus I just don't remember the steps exactly because it's been so long, you don't have to go too in depth

Answer 8

for example, I think that the volume should be : (3-2x)(3-2y)(x)
but I'm trying to enter it into my online homework and it isn't working and I'm not sure how to continue from there

Answer 9

Yes, that's not right because you only need to deal with one variable: x

Answer 10

Remember, we're dealing with a square, not a rectangle

Answer 11

so V = x(3-2x)^2

Answer 12

then I would get \[9x-12x^2+4x^3\] i tried that too and it won't work for the part that says expression of the volume

Answer 13

Okay, there are other forms to can write for the expression of V:

\[V = x(3-2x)(3-2x)\]
\[V = x(3-2x)^2\]

Try those

Answer 14

yeahh haha uhm none of them work

Answer 15

and I only have two submissions left

Answer 16

I'm sorry to hear that. I don't know what they want, but the expressions are not incorrect

Answer 17

yeah I didn't think they were wrong either. could you just show me how to write it as a function of x and how I would eventually get what the volume is?

Answer 18

\[V(x) = x(3-2x)^2\]

Answer 19

Try that

Answer 20

mm no that doesn't work

Answer 21

Well, you need to just skip that problem because it only wants one input that no one will be able to figure out

Answer 22

well I mean that is the right beginning, and there's the other parts that still have to be answered

Answer 23

its just not being taken as the right answer for some reason

Answer 24

but I still want to know how to relate to writing it as a function of x and how I would get to the final answer

Answer 25

I can't help you with this if that's the kind of problem you're having. Obviously, the program doesn't like accepting right answers.

Answer 26

haha okay thanks anyway..

Answer 27

maya.y

I hope that the attached solution is what you are looking for.

Answer 28

I don't see anywhere where it says the units has to be in inches

Answer 29

So I don't understand your approach in that regard

Answer 30

Well they can convert to feet if they want to.

Answer 31

i'm just saying...why would you give a solution in terms of inches? What led you to that approach?

Answer 32

Avoids fractions.

Answer 33

Hero,
What do you think the presentation?

Answer 34

It was pretty good but only if you consider your approach. I think it would have been more complete if you converted back to feet at the end

Answer 35

Thanks for the response.