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The above equation is an expression for computing the stand density index from the number of trees per acre and the diameter of the tree of average basal area. Assume that a stand with basal area of 150 square feet (14 m 2) and 400 trees per acre is measured. The dbh of the tree of average basal area D is:
Since the diameter is twice the radius, the "missing" part of the diameter is (2r − x) in length. Using the fact that one part of one chord times the other part is equal to the same product taken along a chord intersecting the first chord, we find that (2r − x)x = (y / 2) 2. Solving for r, we find the required result.
where BA is stand basal area, n is the number of trees, and k is a constant based on measurement units - for BA in ft 2 and DBH in inches, k=0.005454; for BA in m 2 and DBH in cm, k=0.00007854. References
As the definition of the unit contains π, it is easy to calculate area values in circular mils when the diameter in mils is known. The area in circular mils, A , of a circle with a diameter of d mils, is given by the formula: { A } c m i l = { d } m i l 2 . {\displaystyle \{A\}_{\mathrm {cmil} }=\{d\}_{\mathrm {mil} }^{2}.}
Another proof that uses triangles considers the area enclosed by a circle to be made up of an infinite number of triangles (i.e. the triangles each have an angle of dπ at the centre of the circle), each with an area of β 1 / 2 β · r 2 · dπ (derived from the expression for the area of a triangle: β 1 / 2 β · a · b · sinπ ...
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 formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is: [6] A = 4πr 2 (sphere), where r is the radius of the sphere. As with the formula for the area of a circle, any derivation of this formula inherently uses methods similar to calculus.
In this context, a diameter is any chord which passes through the conic's centre. A diameter of an ellipse is any line passing through the centre of the ellipse. [7] Half of any such diameter may be called a semidiameter, although this term is most often a synonym for the radius of a circle or sphere. [8] The longest diameter is called the ...
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