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

[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" ?