Transformation from 2D to 3D equationl?

Question

Under microscope two dimensional features such as area of a particle can be measured. But this has to be converted to three dimensiomal measurement. Can you do it by any mathematical trnsformation?

Answer 1

There is no exact mathematical transformation possible that will give you the 3D surface of an object, when given only the 2D area of an orthogonal view of it. However, as a rough rule of thumb, a ball-like particle's 3D surface area is 4 times greater than what you see in a flat 2D view of it. The reason for this is seen by comparing the area formulas for a flat 2D circle and a 3D ball, both of same radius:

Area of 2D circle..............π r ²
Area of 3D sphere.......4 π r ²

Answer 2

Why wouldn't the area of a particle be 3 dimensional?...2D would only measure a cross section.