How do you determine surface area when given volume?

Answer 1

You cannot, unless you know what the shape is. For a very few regular shapes, the volume can provide information on the linear dimensions of the object. But even for something as simple as a cuboid (but not a cube), that does not work - there are an infinite number of possible measures for the length/breadth/height which will give the same volume.

Once you have these linear dimensions, determining the surface area is a lot more straightforward.