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For n trees, QMD is calculated using the quadratic mean formula: where is the diameter at breast height of the i th tree. Compared to the arithmetic mean, QMD assigns greater weight to larger trees – QMD is always greater than or equal to arithmetic mean for a given set of trees.
The area in circular mils, A, of a circle with a diameter of d mils, is given by the formula: {} = {}. In Canada and the United States, the Canadian Electrical Code (CEC) and the National Electrical Code (NEC), respectively, use the circular mil to define wire sizes larger than 0000 AWG .
To calculate trunk volume, the tree is subdivided into a series of segments with the successive diameters being the bottom and top of each segment and segment length being equal to the difference in height between the lower and upper diameters, or if the trunk is not vertical, the segment length can be calculated using the limb length formula ...
Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
The area-equivalent radius of a 2D object is the radius of a circle with the same area as the object Cross sectional area of a trapezoidal open channel, red highlights the wetted perimeter, where water is in contact with the channel. The hydraulic diameter is the equivalent circular configuration with the same circumference as the wetted perimeter.
Thus, the outer diameter of a catheter in millimeters can be calculated by dividing the French size by 3. [2] For example, a catheter with a French size of 9 would have an outer diameter of approximately 3 mm. While the French scale aligns closely with the metric system, it introduces redundancy and the potential for rounding errors.
Since the area of the rectangle is ab, the area of the ellipse is π ab/4. We can also consider analogous measurements in higher dimensions. For example, we may wish to find the volume inside a sphere. When we have a formula for the surface area, we can use the same kind of "onion" approach we used for the disk.
Using radians, the formula for the arc length s of a circular arc of radius r and subtending a central angle of measure 𝜃 is =, and the formula for the area A of a circular sector of radius r and with central angle of measure 𝜃 is A = 1 2 θ r 2 . {\displaystyle A={\frac {1}{2}}\theta r^{2}.}
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