Melting Iceberg Problem

[MelThyHonest]

Assume that the iceberg is a cube of 1331000m³ and that it melts uniformly so that a top layer of 1m is lost each day.

Now the first actual question asked to find an expression for the volume of the iceberg after n days, but what confuses me is I'm not exactly sure what it means by 'melting uniformly so that a top layer of 1m is lost each day' does it mean it retains the shape of a cube so 1m would melt off of each dimension? In this case 110 is the L/W/H so would I take off 1m from all of them per day or would I take of 1m for each face so 2m per dimension? Or am I over thinking this and it's just a linear expression where I'd take 1m off the height only.

These are the three expressions I'd expect it to be from:
V=1331000-12100n (the linear ex)
V=(110-n)³
V=(110-2n)³

Please help I can't really go ahead until I understand the beginning

Edit: My apology I did make a typo the iceberg is a cube of 1331000m^​3

 

[Deleted member 4993]

Assume that the iceberg is a cube of 1331000m and that it melts uniformly so that a top layer of 1m is lost each day.

Now the first actual question asked to find an expression for the volume of the iceberg after n days, but what confuses me is I'm not exactly sure what it means by 'melting uniformly so that a top layer of 1m is lost each day' does it mean it retains the shape of a cube so 1m would melt off of each dimension? In this case 110 is the L/W/H so would I take off 1m from all of them per day or would I take of 1m for each face so 2m per dimension? Or am I over thinking this and it's just a linear expression where I'd take 1m off the height only.

These are the three expressions I'd expect it to be from:
V=1331000-12100n (the linear ex)
V=(110-n)³
V=(110-2n)³

Please help I can't really go ahead until I understand the beginning

I agree that the problem is ill-posed.

However, in your problem statement you sate that "....the iceberg is a cube of 1331000 m....." (not m³). Whatever the number, let's indicate that each side of the cube is L m long.

I would assume V = (L -2n)³

 

[stapel]

Assume that the iceberg is a cube of 1331000m and that it melts uniformly so that a top layer of 1m is lost each day.

Now the first actual question asked to find an expression for the volume of the iceberg after n days, but what confuses me is I'm not exactly sure what it means by 'melting uniformly so that a top layer of 1m is lost each day' does it mean it retains the shape of a cube so 1m would melt off of each dimension?

Yes. While this is utterly unrealistic, you're in math class, not "real life", so you've been given this simplifying assumption.

In this case 110 is the L/W/H so would I take off 1m from all of them per day or would I take of 1m for each face so 2m per dimension?

I would assume the latter. If a top layer is being lost "uniformly", then you're losing that layer all over. This will cause a loss of two meters in each "direction".

These are the three expressions I'd expect it to be from:
V=1331000-12100n (the linear ex)
V=(110-n)³
V=(110-2n)³

I'm sorry, but I don't understand what you mean by "expect it to be from" or the three equations you've posted?

Consider the algebra:

. . .original dimensions:
. . . . .$\displaystyle \sqrt[3]{1,331,000\,}\, =\, 110$
. . . . .L, H, W: 110 meters on day 0

Edit: The above, as noted in the previous reply (posted while I was typing), may not be correct, if my assumption of a typo in your post is not correct.

. . .dimensions on day n:
. . . . .(original value) less (one meter per day)*(number of days)
. . . . .$\displaystyle 110\, -\, 1n$

What then would be the volume expression on the n-th day?

 

[MelThyHonest]

So my thought behind the three equations were based on the first question it asked me to find an expression for the volume(V) after (n) days.
Eq 1. Is what I believe it would be if the question is saying that 1m is taking off the top of the cube only so 1m*110m*110m=12100m³ and then just multiplied but however many days.
Eq 2. Is what I believe it would be if the question is saying that 1m is taking off the height width and length (since that might be what was meant by 'melting uniformly')
Eq 3. Is what I believe it would be if the question is saying that 1m is taking from each face.
I doubt the answer is Eq 1 since it doesn't really fit the theme of the questions (being linear) I can't tell whether or not Eq 2. or Eq 3. would be correct


1. V=1331000-12100n (the linear ex)
2. V=(110-n)³
3. V=(110-2n)³

 

[Ishuda]

Assume that the iceberg is a cube of 1331000m³ and that it melts uniformly so that a top layer of 1m is lost each day.

Now the first actual question asked to find an expression for the volume of the iceberg after n days, but what confuses me is I'm not exactly sure what it means by 'melting uniformly so that a top layer of 1m is lost each day' does it mean it retains the shape of a cube so 1m would melt off of each dimension? In this case 110 is the L/W/H so would I take off 1m from all of them per day or would I take of 1m for each face so 2m per dimension? Or am I over thinking this and it's just a linear expression where I'd take 1m off the height only.

These are the three expressions I'd expect it to be from:
V=1331000-12100n (the linear ex)
V=(110-n)³
V=(110-2n)³

Please help I can't really go ahead until I understand the beginning

Edit: My apology I did make a typo the iceberg is a cube of 1331000m^​3

My take on the situation:

First, I would have thought that staples's

...dimensions on day n:
.........(original value) less (one meter per day)*(number of days)
.........[FONT=MathJax_Main]110[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Math]n[/FONT]

was correct. That is there is a front, back, left, right, bottom, and top side to the iceberg and the top lost 1 m per day uniformly. So L and W stayed constant and H varied as 110-n or
(Answer 1) V=110² (110-n)= 1331000 - 12100 n

However, if the correct answer must be one of the 3 answers given and the above is not the answer, I believe that the question should be re-written more clearly where
(1)the 'top' means 'one side of each of the front/back, left/right, and top/bottom pair', i.e. the top side of each of the 3 pairs In that case each of the L, W, and, H vary as 110-n and
(Answer 2) V=(110-n)³
OR
(1)the 'top' means 'the outside layer of each of the front, back, left, right, top, and bottom'. In that case each of the L, W, and, H vary as 110-2n and
(Answer 3) V=(110-2n)³

I also certainly agree that the problem is ill-posed.

EDIT: So, as Alice said 'everybody wins and everyone must have prizes'