Surface Area or Volume

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Pokemon

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There are two boxes cuboid and cube, to find out which box requires lesser material to make, what should be found out? Is it Volume or Surface area.
I far as I checked surface area is calculated but why can't we calculate the volume to solve this question.
 
Pokemon said:
There are two boxes cuboid and cube, to find out which box requires lesser material to make, what should be found out? Is it Volume or Surface area.
I far as I checked surface area is calculated but why can't we calculate the volume to solve this question.
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Volume matters when comparing the capacity of the boxes, not the amount of flat material the boxes are made of.
 
Correct me if I'm wrong, but isn't a cube a cuboid with all 6 sides being equal size ?
 
jpigg55 said:
Correct me if I'm wrong, but isn't a cube a cuboid with all 6 sides being equal size ?
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You are correct. But how does it matter in the question of what we need to calculate, volume or surface area?
 
It doesn't.
For any given volume being equal between the two, the surface are would be the same for both.
With volume being L*W*H and surface area of each side being L*W. So if volume of both are equal, then the combined surface area of all sides would also have to be equal.
So the only variable would be the dimensions of the material used to construct each and would depend on the amount of wastage, if any.
 
jpigg55 said:
With volume being L*W*H and surface area of each side being L*W. So if volume of both are equal, then the combined surface area of all sides would also have to be equal.
Click to expand...
Let's verify this statement.
Consider a cube with side 2 (volume would be 2*2*2 = 8) and a cuboid with sides 1, 2, 4 (same volume, 1*2*4 = 8).
What are their surface areas?
 
jpigg55 said:
It doesn't.
For any given volume being equal between the two, the surface are would be the same for both.
With volume being L*W*H and surface area of each side being L*W. So if volume of both are equal, then the combined surface area of all sides would also have to be equal.
So the only variable would be the dimensions of the material used to construct each and would depend on the amount of wastage, if any.
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Are you sure about that? If the V =L*W*H, then what would the surface area be. If the sides were all cuberoot(L*W*H) then what would the surface area be. Are you getting the same results?
 
Your example is just looking at the 2 dimension aspect of the problem, not 3 dimension.
In your example, the cuboid would have 2 sides that are 1x2 (2*1*2=4) and 4 sides that are 2x4 (4*2*4=32) thus equaling 36 total square inches.
The cube, on the other hand has all equal sides so 6*2*2*2=36 total square inches.
Both the same.
 
jpigg55 said:
Your example is just looking at the 2 dimension aspect of the problem, not 3 dimension.
In your example, the cuboid would have 2 sides that are 1x2 (2*1*2=4) and 4 sides that are 2x4 (4*2*4=32) thus equaling 36 total square inches.
The cube, on the other hand has all equal sides so 6*2*2*2=36 total square inches.
Both the same.
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To find surface area most people use 2 dimensions.
 
Jomo said:
To find surface area most people use 2 dimensions.
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Yes, 2 dimensions for area of each side, but you also have to take the total number of sides into consideration for total surface area.
So back to the example given, the cuboid could have 2 sides that were either 1x2 or 2x4. For a given volume though, the other 4 sides would use the other dimension for volume used. Hence, 4 sides that would be either 2x4 or 1x4.
No mater how you slice it, if both volumes are equal, the total surface area of all 6 sides will be 36 square inches, for the given example.
 
jpigg55 said:
Your example is just looking at the 2 dimension aspect of the problem, not 3 dimension.
In your example, the cuboid would have 2 sides that are 1x2 (2*1*2=4) and 4 sides that are 2x4 (4*2*4=32) thus equaling 36 total square inches.
The cube, on the other hand has all equal sides so 6*2*2*2=36 total square inches.
Both the same.
Click to expand...
I think we are not on the same page regarding what a cuboid is. Do you think it requires 2 faces to be squares? I am not sure about that, but let's assume that this is the case.
Let's compare:
1. Cube 2x2x2. Volume = 8. Surface area: 6 2x2 faces, 6*4 = 24
2. Cuboid 1x1x8. Volume = 8. Surface area: 2 1x1 faces, 4 1x8 faces, 2*1 + 4*8 = 34.
 
jpigg55 said:
Yes, 2 dimensions for area of each side, but you also have to take the total number of sides into consideration for total surface area.
So back to the example given, the cuboid could have 2 sides that were either 1x2 or 2x4. For a given volume though, the other 4 sides would use the other dimension for volume used. Hence, 4 sides that would be either 2x4 or 1x4.
No mater how you slice it, if both volumes are equal, the total surface area of all 6 sides will be 36 square inches, for the given example.
Click to expand...
It is simple, what you are saying is not true. I am waiting to hear your response to what Lev888 said and where the mistake is in that post.
 
As far as Lev888, I was mistaken.
As for the OP, calculating volume isn't equal to surface area.
The answer lies in the "Surface Area to Volume Ratio", but there is no one formula to correlate between the two unless they are the same shape.
In the OP, surface area for a cube is 6X^2, whereas for the cuboid it's 2XY + 2XZ + 2YZ.

Seems a little odd since one could take a 2x2x2 cube, cut in half along 2 axes, and end up with four 1x1x2 pieces. Stack the pieces end to end and you end up with a 1x1x8 piece though doing so loses 6 of the 1x1 ends making you think the surface area would be less, yet it ends up being greater.
 
jpigg55 said:
Seems a little odd since one could take a 2x2x2 cube, cut in half along 2 axes, and end up with four 1x1x2 pieces. Stack the pieces end to end and you end up with a 1x1x8 piece though doing so loses 6 of the 1x1 ends making you think the surface area would be less, yet it ends up being greater.
Click to expand...
This happens because you are creating more surfaces by cutting than losing them by stacking.
 
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