Question

an open rectangular box with a square base is to be made from 64 ft^2 of material. What dimensions will result in a box with the largest possible volume?

Answer 1

nope

Answer 2

3d

Answer 3

it would have to be seeing as its asking for volume

Answer 4

haha yeah thats the question...what are the dimensions. which you find out using calculus

Answer 5

and i got most of it but when i got to the end it was a irrational number and seemed wrong

Answer 6

no. its a question in calculus...read the question. Thats the entire question.

Answer 7

it can imply that...it doesnt really matter anyway because its just asking for the dimensions when you have the max volume, and that would mean inside the box

Answer 8

If the amount of material used is 64 ft, which would mean thats the surface area, then the volume wouldnt be less than the surface area...

Answer 9

you clearly have no clue what youre doing so just stop lol. I already said this requires calculus, have you even taken calculus ha

Answer 10

its not just some simple middle school word problem...

Answer 11

nniggga

Answer 12

well have you done differentiations and max and min problems...If not then you wont be able to solve this.

Answer 13

man flutterkk ya in the retricehole

Answer 14

man fuqck ya in the acsshole

Answer 15

Youre stupid as pellet

Answer 16

pellet

Answer 17

apparently you cant swear

Answer 18

sorry im not a pro at being a dumbasss and needing to swear at people cause youre stupid

Answer 19

Volume of a rectangular box with dimensions \(x\times y\times z\) is \(V=xyz\). The base is square, so let two of the variables be equal, so that
\[V=xy^2\]
You have \(64 \text{ ft}^2\) of material available, so your surface area is given by
\[\begin{align*}A&=2xy+2xz+2yz-yz\\
64&=4xy+y^2\end{align*}\\\text{(since we're letting }y=z\text{ and one of the faces is missing})\]
Find an expression for one of the variables in terms of the other (\(x\) in terms of \(y\) is easier):
\[x=\frac{64-y^2}{4y}\]
So you have
\[V=\frac{(64-y^2)y^2}{4y}=\frac{(64-y^2)y}{4}\]
Find the critical points of \(V\) and show that a max indeed occurs at the critical point (first derivative test).

Answer 20

yeah i got up to that part and took the derivative of the volume/v and it was a radical and seemed wrong but idk

Answer 21

The optimizing value can be anything, so long as it's realistic. It can't be negative, zero, or infinite.