I have a number of trees in a stand and I
want to estimate the volume of the trees. One tree in particular
is **43.5**m high, and the dbh (diameter at basal
height) is **2.48** m. The **dbh** is
the diameter of the tree at a height of about
**1-2**m above the ground. Below this point the tree
trunk really spreads out and is ignored.

## Solution:

Most of the valuable wood is in the trunk of the tree. The
shape of the trunk can be approximated by a cone whose height is
that of the tree, and whose basal diameter is the dbh of the
tree.

### Setting up the problem - translating from words to symbols:

Let *h* be the height of the cone
and *r* be its radius at the base. The
formula for the volume of the cone is

### Calculations:

The radius is half the diameter, or *r =*
2.48/2 = 1.24 m and *h =* 43.5
m. If we substitute these numbers into the equation
for the volume, we get

Hence the estimated volume of the tree
is 70.0 m3