The Open Top Box

SydneyRoverP6B

SydneyRoverP6B

Well-Known Member
Staff member
A box with no top must have a base twice as long as it is wide, and the total external surface area of the box is to be 54 square cm. What dimensions do you make the box,.( length, width and height ) in order that the box will possess the greatest possible volume for the set surface area?

Ron.
 
Hello Richard,

What do you mean by 3? You are correct in that the box has no top, so the external surface area is composed on the base, two ends and two sides. A certain set of dimensions will deliver the largest possible volume for the given surface area of 54 square cm.

Ron.
 
The biggest volume for a 6 sided shape would be a cube, and if you counted the top, there would be 6 sides.

54/6 = 9 so the sides would all be 3x3.



The shape with the biggest volume per area is a sphere, which is why elephants have big ears.

(nothing to do with Noddy refusing to pay the ransom :shock: )
 
quattro wrote,..
The biggest volume for a 6 sided shape would be a cube, and if you counted the top, there would be 6 sides.

54/6 = 9 so the sides would all be 3x3.
Click to expand...

Hello Richard,

You can't count the top though, as the box only has 5 faces, and the base must be twice as long as it is wide. It is not a cube.

Ron.
 
corazon wrote,..
3 wide, 2.25 high, and 6 long
Click to expand...

Hello corazon,

Sorry, but those figures do not provide a surface area of 54 square cm which is required in this case. How did you determine those figures?

Ron.
 
SydneyRoverP6B said:
quattro wrote,..
The biggest volume for a 6 sided shape would be a cube, and if you counted the top, there would be 6 sides.

54/6 = 9 so the sides would all be 3x3.
Click to expand...

Hello Richard,

You can't count the top though, as the box only has 5 faces, and the base must be twice as long as it is wide. It is not a cube.

Ron.
Click to expand...

Didn't read that bit :oops: - will have a look later - have to do some work or I get told off
 
quattro wrote,...
have to do some work or I get told off
Click to expand...

That's a pity,...this is much more enjoyable. I always do the problems before I post them, and in this case there is a reasonable amount of work to obtain the answer, and certainly no guessing or trial and error is involved.

Ron.
 
I have a width of 3, length (twice) of 6 and a height of 2

Area = 54 volume = 36
 
Hello Richard,

Yes,..that is correct... :D These problems really stimulate the mind, and that is a great.

Ron.
 
Classicus wrote,...
What relevance, if any, do Ron's puzzles have to P6 Rover ownership and maintenance?
Click to expand...

Hello Classicus,

Nonething what so ever, that is why I place them here in the Lounge section where all manner of unrelated topics can be discussed, from Garage doors to the weather. Afterall, does it not say....the place to talk about everything else?

Ron.
 
Classicus said:
What relevance, if any, do Ron's puzzles have to P6 Rover ownership and maintenance?
Click to expand...

It's fun, and gives Ron and Richard a chance to show how good they are at cheating... I mean, solving puzzles! :p
 
darth sidious said:
Classicus said:
What relevance, if any, do Ron's puzzles have to P6 Rover ownership and maintenance?
Click to expand...

It's fun, and gives Ron and Richard a chance to show how good they are at cheating... I mean, solving puzzles! :p
Click to expand...

Oi!! I resemble that remark!
 
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