is it possible for two boxes to have the same volume, but different surface areas?

Answer 1

Yes - 2 boxes can have the same volume but different areas

take an example of a rectangular box

length = l
height = h
breadth = b
edit - (note these are outside dimensions - so wall thickness does not matter)

volume = v
area = a

volume = l*h*b
area = 2*h*l + 2*h*b + 2*l*b

now solve for a

a = v/2 * (1/l + 1/b + 1/h)

which has multiple solutions for the same v

here are some worked results to demonstrate the point

length height breadth volume area
l h b l*h*b 2*l*h+2*l*b+2*h*b

1 1 0.5 0.5 4
1 2 0.25 0.5 5.5
0.5 2 0.5 0.5 4.5
1 4 0.125 0.5 9.25
2 2 0.125 0.5 9

edit - see how the volume is 0.5 cubic units while the surface area varies from 4 to over 9 square units

Answer 2

Yes. Take a box 1' cubed. It has 1 cubic foot of volume space. Take another box 2'x1'x.5'. The theoretical interior volume is still 1 cubic ft. However, the exterior of the cube has a surface area of 6 square ft. The rectangular box has an area of 5 square ft.

Answer 3

Yes. Start with any two boxes of differing geometric shape (ie., not similar) Adjust the dimensions of either box so that its volume matches the other box while, simultaneously its shape remains similar to the original shape. If you calculate the surface areas of both boxes they will be different.

Look at it this way, volume is a third-order function while area is a second-order function. If we adjust the variables of two different third-order functions so they return the same result, then the two second-order functions, based on those same variables, cannot possibly return identical results.

Answer 4

Of course it is

think of a 'box' with the smallest surface area to volume ratio and you have a sphere.

squash that sphere out into a long long sausage shape, you keep the volume but the surface area is greatly increased.

Answer 5

Yes, however "box" in your question is not well defined. Let's assume that the "box" is more than just a mathematical "box" e.g. a cardboard "box." So, you could have a cardboard "box" with thick walls and a cardboard "box" with thin walls. Then there is an internal surface area and an external surface area. The boxes could have the same volume, but different external surface areas due to the thickness of the walls. Sometimes you have to think outside the "box."

Answer 6

I would have to say "it depends"

Take for example a rectangle, in this case, NO:
The Volume is the base area multiplied by the height. Everything relates to everything else, and if the 2 boxes have the same volume then they must have the same surface area.


What about a balloon??? Especially one that is partly filled with water, this might have the same surface area---I think??!!!

That's why I conclude that it depends on the situation. In the case of boxes, my (final) answer is NO.

Hope this helps!!!!

Answer 7

no - if the volume is different the surface area will change.

Surface area will determine the volume.

Answer 8

yes

Answer 9

depends on your wall thickness.