Help Me with Maths B

[Osmosis]

Ok so this is due tomorrow (it's part of my Maths B assignment) and I just can't do it.

 <cool372> Explore the dimensions of the cheapest* possible carton to hold 60 individual fruit drink containers if each container is a rectangular prism with outside dimensions of 11cm * 6cm * 4cm
[16:10:47] <cool372> A) You should first explore (using the derivitive) the cheapest carton that is SQUARE BASED and holds the same volume of the 60 fruit drink containers
[16:10:32] <cool372> B) Using your observations from part A) (or otherwise) make your final decision on carton Dimensions fully justifying your answer
[16:10:51] <cool372> * Assume the the cheapest possible carton is the one of least surface area

Any help would be loved The solution would be an orgasm.

Once again, if you don't know, don't post

 

[Phil]

Wouldn't you start off with the minimum base, which would be;

11*4 which is 1 container in the base. To have 11*4 and hold 60 containers the box would obviously have to be 4*60 in height.
Then work out it's surface area.

4*4 = 16.
11*4 = 44
11*6 = 66

= 116. That gives you the surface are for one box

116*60 (the number of boxes you have) = 6960 com of surface area in this container.

Now try it with other base areas i'm assuming.

(This is a guess m8).

Hope i helped.

 

[Osmosis]

Thanks its a start. Common Maths geniuses we have like 10 hours

 

[Dorito]

Yeah, sorry, didn't see your PM cool372. Been quite busy lately, I'll post back in a bit with my answer.

Below is just so I can read it in a clearer view so disregard it until I post further.

Explore the dimensions of the cheapest* possible carton to hold 60 individual fruit drink containers if each container is a rectangular prism with outside dimensions of 11cm * 6cm * 4cm
A) You should first explore (using the derivative) the cheapest carton that is SQUARE BASED and holds the same volume of the 60 fruit drink containers
B) Using your observations from part A) (or otherwise) make your final decision on carton Dimensions fully justifying your answer
* Assume the the cheapest possible carton is the one of least surface area

EDIT: Is there anything more to the question? Or is that all it gives you?

 

[Cruel__Machine]

For the record, what math is that? Seems like Algebra II. I am in Trig/ Calc Hon. right now.

Did you use derivatives in algebra? lol
Seem like calculus to me (or pre-calc).
You just have to find out the derivative of the equation of the surface area and find the critical points (to get the min/max) values.
I'd make an answer, but I'm just about to leave. Tough luck lol. When I get back it'll probably be too late.

 

[Cruel__Machine]

Alright...
It seems that for B) they just want you to explain some reasoning. I think they basically want you to notice that a cube has the ideal surface area - volume ratio. Because if you do A) with a carton with a square base, you'll just end up with a cube (each side being the cube-root of 15,840, which is the complete volume). But that comes out to like 25.11 and such a cube wouldn't fit those 60 containers.

I'd guess a dimension like 30-24-22... closest to the cube that I can think of. And I could explain my reasoning too... but I don't have the assignment, so no reason

EDIT: oh ya, tell us the answer when u get it

 

[Geόrge]

So how did you go? Well? What was the answer...

 

[Xjaa]

r u meh kiddain? what grade are you in?

can we just use AT = (combined bhl)