The Method of Mechanical Theorems convenient to use a little bit of coordinate geometry. If a sphere of radius 1 is placed with its center at "x" = 1, the vertical cross sectional radius formula_2 at any "x" between 0 and 2 is given by the following formula: The mass of this cross section, for purposes of balancing on a lever, is proportional to the area: Archimedes then considered rotating the triangular region between "y" = 0 and "y" = "x" and "x" = "2" on the "x"-"y" plane around the "x"-axis, to form a cone. The cross section of this cone is a circle
Tree volume measurement slight tension between the poles holds them steady against the trunk. Tents stakes wedged in the bark can also be used to level and steady the frame. One end is designated the y axis, and the adjacent side the x axis. Measurements are made with a carpenters tape from the frame to the edge of the trunk and the profile of the trunk shape is plotted. The data is then entered into a trapezoidal area function in a spreadsheet and converted into cross sectional area so as to calculate the equivalent circumference to use in the volume formula. Many trees