Rattlesnake asks: > I'd like to know how to calculate volume using 2 measures of either area > or perimeter. I have 2 digital photographs, one provides a top view and > one provides a side view, of the object that I want to calculate the > volume of. I need to know if there's a mathematical formula that I can > plug in area from the top view & area from the side view to get volume. I > can add photos later if need be.
There is no simple answer for this question. It depends on the shape of the object. If the object under question is a regular solid (a cube, a cylinder, a sphere, etc.), then the equations to calculate its volume are elementary and are found in any basic math book. For example, a cube's volume is merely its height x width x depth. However, if the object is irregular in its shape in both the plan and side views, you may not even have enough information to accurately calculate its volume. Critical portions of the object may be missing from these views (think of an upside down coffee cup taken from a perspective where you cannot see the handle in the side view. From these two views, bottom and side, you would never know that the cup is primarily hollow and the handle is essentially so as well). But even if you feel that side and plan views represent an accurate portraiture of the object, but the object is still irregular, then you will need to use some form of integration to calculate its volume, either numerically done or as a closed form calculation, even though, has been said in the last several days, real biologists don't do calculus. Often approximations of a series of regular solids are used in place a well-defined integral. As the physicist once said when talking about radiative heat transfer in cattle, "Assume a spherical cow..." It may sound foolish, but to some great degree, how you calculate the volume depends on the necessary accuracy you require in your answer. Wirt Atmar
