Can you solve the volume of a cube with unequal heights?

[vrmuth]

What are you on about? IF the diagonal is known then there is NOT "another" solution. The statement that there has to be two solutions is based on not knowing which diagonal is being used so you have to solve for both.

what do you mean ? two different formulas or one formula that suits both cases?

 

[DaveC426913]

what do you mean ? two different formulas or one formula that suits both cases?

It's one formula (or possibly one algorithm, which is several steps of formulae), that will leave it up to the user to plug in values. The user has a choice of which values she plugs in, based on what design she intends to solve for. The onus will be on the user to decide, at solving time, where the diagonal is.

 

[phinds]

what do you mean ? two different formulas or one formula that suits both cases?

The "general" solution is TWO solutions (or a "solution" that gives two answers) but if you SAY which diagonal you are talking about then there is only one solution (yes, one formula) needed.

 

[vrmuth]

It's one formula (or possibly one algorithm, which is several steps of formulae), that will leave it up to the user to plug in values. The user has a choice of which values she plugs in, based on what design she intends to solve for. The onus will be on the user to decide, at solving time, where the diagonal is.

The "general" solution is TWO solutions (or a "solution" that gives two answers) but if you SAY which diagonal you are talking about then there is only one solution (yes, one formula) needed.

very good , thanks dave that's what exactly i was trying to say ( because of my poor communicatin skill i was unable ) you know my formula is such a one ?, the user must choose h2 and h4 as the heights of the end points of the diagonal without worrying about whether its a wedge or a valley . if its a valley the other two heights h1 and h2 will be taller and shorter if its a wedge , the same formula will take care of everything b'cause i derived the formula for any values of h1 and h3 , the formula for area of a rectangle(with a>b) hold good for area of a square and we don't have a different formula for b>a

 

[vrmuth]

if its a valley the other two heights h1 and h2 will be taller and shorter if its a wedge...

sorry it's h1 and h3

 

[logics]

...which I plan on working on this weekend myself when I have free time from my homework...

... the order of the heights won't decide whether is there a wedge or a valley on the top surface

PF policy is to give hints, not solutions. I was waiting for OP to turn up: I want to give him a chance to solve the problem himself. In the meanwhile, I'll give him [and you] another hint.
The order, of course, does not decide but every sequence has only one possibility. General solution is very simple: just a few symbols.

 

[vrmuth]

PF policy is to give hints, not solutions.

yes, but this not a home work :), and the op also not a math student it seems , so he may not be able to solve even if you give him hints

 

[DaveC426913]

yes, but this not a home work :), and the op also not a math student it seems , so he may not be able to solve even if you give him hints

Technically he's got a point though. Regardless of whether an OP is a student or not, we are not supposed to solve homework-like problems. Students read the forum too.

But I felt this was an exception since I see it as not a homework problem (that's the debatable point) But we didn't actually know if there was a solution. Also because it was really interesting.

 

[vrmuth]

if you are given the surface area of all sides, including the base, except for its top? The sides of this object would be four trapezoids

Will the area of all the sides be given seperately in order? ,There are infinite number of possible values of h , so any one value of h must be chosen(say k) and then the resulting volume will depend upon it (k) , so for each value of fixed h we 've a different volume , all having the given suface area , in otherwords there are infinite volumes for the "one set of surface area" ( i will give the proof if allowed )

The problem says: given the "surface areas" of all sides: we can deduce the values of, but we need to know the order of h _1,2,3,4

how can we deduce ?

The order, of course, does not decide but every sequence has only one possibility. General solution is very simple: just a few symbols.

what sequance you are talking about ? i cann't logic it

But I felt this was an exception since I see it as not a homework problem (that's the debatable point) But we didn't actually know if there was a solution. Also because it was really interesting.

yes its geting more and more interesting now

 

[DaveC426913]

Will the area of all the sides be given seperately in order? ,There are infinite number of possible values of h , so any one value of h must be chosen(say k) and then the resulting volume will depend upon it (k) , so for each value of fixed h we 've a different volume , all having the given suface area , in otherwords there are infinite volumes for the "one set of surface area" ( i will give the proof if allowed )

how can we deduce ?

I thought we'd settled this. We are given the height of the four corners, in order. The OP has base and all sides already built, so he knows what they are.

 

[vrmuth]

I am trying to map the the volume of space shaded by irregular objects with a light source coming from a given angle...

I am not able to understand this fully , Can i have more information and example on this ?

 

[phinds]

I am not able to understand this fully , Can i have more information and example on this ?

I have to agree, this is VERY odd wording. I think everyone got interested in solving the immediate problem of finding the volume of the enclosed figure he drew and no one commented on this part of it.

I too do not get how you "map a volume of space" in this regard or why it would be meaningful to do so.

 

[DaveC426913]

I have to agree, this is VERY odd wording. I think everyone got interested in solving the immediate problem of finding the volume of the enclosed figure he drew and no one commented on this part of it.

I too do not get how you "map a volume of space" in this regard or why it would be meaningful to do so.

Well, if we take it literally, it is simply the entire volume that is in the shadow of an object lit by a single light source.

 

[phinds]

Yeah, that makes sense, but what could be the point? I was primarliy confused because I somehow go it in my head that he had said that the light shines UP, so I was (clearly incorrectly) envisioning an infinitely expanding cone out into space with a rectangular (or trapazoidal) cross section.

I could see it making sense if he was looking for the AREA on the ground that is covered by the shadow, but the VOLUME ?

 

[DaveC426913]

Yeah, that makes sense, but what could be the point? I was primarliy confused because I somehow go it in my head that he had said that the light shines UP, so I was (clearly incorrectly) envisioning an infinitely expanding cone out into space with a rectangular (or trapazoidal) cross section.

I could see it making sense if he was looking for the AREA on the ground that is covered by the shadow, but the VOLUME ?

I don't know why he wants this. Perhaps he is studying architecture of large buildings on nearby greenhouses. As his OP says:

I am trying to map the the volume of space shaded by irregular objects with a light source coming from a given angle (so I can ask an interesting sunlight competition question for my undergraduate senior project in plant ecology).

 

[vrmuth]

I thought we'd settled this. We are given the height of the four corners, in order. The OP has base and all sides already built, so he knows what they are.

No Dave, the op doesn't know the heights , he is giving us only the surface areas.And moreover, while the volume is not uniquely determined by the surface area and his objective is to find volume , i don't know why he is going for surface area,what's his difficulties in measuring the heights.He might have satisfied by your formula for the trivial case but his problem still gives lots of other interesting ideas.For eg. even if he gives surface areas there exist infinite set of values for h's and that too under a condition if A1+A3=A2+A4 similar to h1+h3=h2+h4, otherwise no solution at all (isn't it interesting ? )

if you are given the surface area of all sides, including the base, except for its top?...field measurements could yield an average volume that would be represented by a shape similar to the one I've described (because I believe I've already figured out a way to find the area of all the sides and the base).

 

[DaveC426913]

No Dave, the op doesn't know the heights , he is giving us only the surface areas.

I did not get that impression from the OP's message. Though I grant that yours may be a valid interpretation.

 

[logics]

... op doesn't know the heights , he is giving us only the surface areas.

can anyone give "A" [= B(h+h')/2] without knowing "h',h" ?