Frustum of a Cone  

Date: Thurs, Nov 13 2008 6:39 pm
From: "Edward Frank"

We measure the volume of a tree by measuring the diameter or girth of the tree at different heights. The length between the measurements, and the respective girth or diameter at the top and bottom of that segment is used to calculate the volume of that segment of the tree. These segments are treated like cones with their tips cut off- a frustum of the cone. The formula for calculating the volume of the frustum is as Bob stated below. So you stack all these sections together and that gives you the volume of the tree. The diameters are measured by actually climbing the tree or using various electronic instruments to measure the girth from the ground. There are many documents about the volume measurement process on the website  , and well a a brief outline in the ENTS Tree Measuring guidelines .

Ed Frank

----- Original Message -----
Sent: Thursday, November 13, 2008 8:36 PM
Subject: [ENTS] Frustum of Cone

A section of a geometric solid like a cone formed by passing horizontal parallel planes through the solid generates a frustum. Practically speaking when applied to tree trunks, frustums are just sections of the trunk. There are formulas to compute the volumes of frustums of different solids. If D1 and D2 are diameters of the top and bottom sections and H is the height of the frustum, the volume is given by:

V = H*PI/12*[D1^2 + D2^2 + D1*D2]