While finding the exact size and volume of a large column can seem rather difficult at first glance, it is actually quite easy given the application of some practical geometry and a few tools. Architects since the time of the ancient Greeks have been measuring columns using similar methods, most famously in the construction of the Pantheon. However, the following techniques are just as useful when measuring a steel column for your own building project.
Things You'll Need
Place your steel column in a sunny place. Place your ruler beside it so that they both cast a shadow, with the ruler's shadow being proportional to its one foot height. Measure and record the lengths of both shadows with the yardstick. Designate the length of the column's shadow as "x" and that of the ruler as "y."
Form a proportion: x/y = h/.333. Solve for "h," the height of the column with .333 being the height of the ruler in yards. The value for h you obtain can then be used to solve for the volume of the column.
Wrap your string around the column on a level plane so that its two ends meet on the other side. Mark where the ends met and measure the portion of your string that was wrapped around the column in yards. This value is C, the circumference of your column.
Using the formula for the circumference of a circle, C = 2πr, solve for r, the radius of the circle that makes up the base of your column. This can be done by dividing the number C you obtained by 6.28, an approximate value for 2π.
Find the volume of the steel column, "V," by plugging the values you found for r and h into the formula V=πhr^2. This will give you the volume of the column in yards squared.
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