Question

A large stand of fir trees occupies 24 hectares. The trees have an average density of 1 tree per 20m squared. A forester estimates that each tree will yield 300 board-feet. Estimate the yield of the stand if one-tenth of the trees are cut. ​

Answer 1

Answer:

The yield of the stand if one-tenth of the trees are cut is 360000 board-feet.

Step-by-step explanation:

First, let is find the total amount of fir trees that occupies the area of 24 hectares. (1 hectare = 10000 square meters)

$n = \sigma \cdot A$

Where:

$\sigma$ - Surface density, measured in trees per square meter.

$A$ - Total area, measured in square meters.

Given that $\sigma = \frac{1}{20}\,\frac{tree}{m^{2}}$ and $A = 24\,h$, the total amount of fir trees is:

$n = \left(\frac{1}{20}\,\frac{trees}{m^{2}} \right)\cdot (24\,h)\cdot \left(10000\,\frac{m^{2}}{h} \right)$

$n = 12000\,trees$

It is known that one-tenth of the tress are cut, whose amount is:

$n_{c} = 0.1 \cdot n$

$n_{c} = 0.1 \cdot (12000\,trees)$

$n_{c} = 1200\,trees$

If each tree will yield 300 board-feet, then the yield related to the trees that are cut is:

$y = S\cdot n_{c}$

Where:

$S$ - Yield of the tress, measured in board-feet per tree.

$n_{c}$ - Amount of trees that will be cut, measured in trees.

If $n_{c} = 1200\,trees$ and $S = 300\,\frac{b-ft}{tree}$, then:

$y = \left(300\,\frac{b-ft}{tree} \right)\cdot (1200\,trees)$

$y = 360000\,b-ft$

The yield of the stand if one-tenth of the trees are cut is 360000 board-feet.