How do you find the surface area of a box?

You can't.

You'd have to know, if not the actual dimensions -- length L, width W, height H -- then at least something that would tell you the shape, like, say, the ratios, L:W:H.

Like some answerers have said, if you knew that it was a cubical box (for which L:W:H = 1:1:1), you could do it.

V = L^3

A = 6 L^2 = 6 V^(2/3) = 6338.46 cm^2

But we don't know that it's cubical. What if the box is twice as wide and 2.5 times as long as it is high? If you knew this, then once again, you could solve for the three dimensions and find the area. But for each set of ratios you'll get a different formula for A in terms of V. [It will always be some constant, C, times V^(2/3) in these cases. And C will always be ≥ 6. So although you can't say what the area is, you CAN say that the minimum possible area is 6 V^(2/3). If you like, I can provide a proof that this is the minimum possible area -- for a rectangular box of volume V.]

But from what you've said, the box doesn't even have to be rectangular. It could be cylindrical, like a hat box. Or a hexagonal prism. And if you look around, eventually you'll find some even more unusual shapes that boxes come in. For a given shape, the formula is, again, always some constant, C, times V^(2/3). [The minimum possible C for any solid is for the sphere, where it is

C = (36π)^(1/3) = ~4.836]

But again, you simply HAVE to know something more than the volume to find the surface area.

P.S. "[number] cm" is not a volume; it's a length. I trust you meant "cm^3."

Christine - No, the area and the volume aren't even of the same physical dimension. Area is in dimensions of length squared; volume is in dimensions of length cubed.

Super Monkey #35 - If, in your first sentence, you change "divide the volume by 3" to "take the cube root of the volume," and change your numbers accordingly, then the rest of your method will give the right answer for a cube (6338.46 cm^2). Unfortunately, we don't know what shape the box is, so this does no good, anyway.

If this is a cube and not a rectangular box, I think I can do it. Since volume is found by multiplying length x width x height (or in the case of a cube, side to the third power), you can find the length of the side by finding the cubed root of your volume (the cubed root of 34,335.9 cm is 32.5 when rounded to the nearest tenth--but keep the actual answer in your calculator to get a more exact answer in the next step). So then you can figure the surface area by computing 6 x side x side (the area of the 6 faces of the cube). Rounding to the nearest thousandth, I figure the answer to be 6,338.457 cm squared. If it is a rectangular box, I have no idea how to figure that out. Good luck!

well, surface area of a rectangular prism is 2*L*W + 2*L*H + 2*H*W (L = length, W = width, H = height)

but, with a cube, it's just 6*L^2 (L = length of one of the sides)

so, if you "box" is a cube, then the volume is V = L^3

34,335.9 = L^3

L = (34,335.9)^(1/3)

and surface are would equal

6*((34,335.9)^(1/3))^2

so, SA =

6*(34,335.9)^(2/3)

First you divide the volume by 3 to get even height, width, and length of the box.

Next you multiply the answer that you got from dividing which is 11,445.3 cm by itself.

Next you should have 130994892.09 cm^2 (130994892.09 square cm).

Finally you multiply that by 6 for all six sides of the box to get 785969352.54 cm2 (785969352.54 square cm)

The volume is the surface area.

If it's a cube; the volume = s³

or s³ = 34335.9 cm³

or s = ³√34335.9 cm

or s = 32.502453464 cm

Now, the surface area = 6s²; so

Surface area = 6 (32.502453464)² cm²

.................. ~ 6338.4568871 cm²