TIMBER Project
Math 121-4255
By: Connor Bennett
Mehrdad Dehmoubed Nasrabadi
Jordan Isom
Gabriel URIOSTEGUI
SEGUN FOLAJIN
Date: November 29th, 2018
Introduction:
In this project, different mathematical calculations were examined to obtain the closest and most
approximate results to a real-life situation where it is necessary to make the decision as to
whether to acquire a plot of land as an investment and generate income by selling the wood
obtained from the trees that are on the land. The idea was to carry out mathematical processes
with pre-established variables on a small plot of land to calculate how much wood could be
obtained from the full plot of land.
Here are the measurements for the plot of land we were assigned:
Plot B: Triangle Sides 52.9ft., 63.4ft., 57.5ft.
Type of
Tree
Number
of Trees
Circumference Angle of
of
Elevation
Representative (degrees)
Tree (in.)
Angle of
Distance
Depression to Tree
(degrees)
(ft.)
Small
Medium
Large
2
5
3
32.0
43.0
57.5
4
3
5
41
33
39
Procedure/Results:
52.9 ft.
63.4 ft.
57.5 ft.
51
83
69
Area of the region:
We use Heron’s Formula to calculate area.
(perimeter: 173.8 ft)
(173.8/2*(173.8/2-52.9)*(173/2-63.4)*(173.8/2-57.5))^0.5 = 1428.75 ft^2
Radius of the trees in the region:
Tree Circumference (32.0 in), M (43.0 in), L (57.5 in)
Radius given circumference: C/2PI/12 (divided by 12 to convert to feet)
Tree Radii: S (0.42 ft), M (0.57 ft), L (0.76 ft)
Height= distance * (tan (angle of elevation) +tan(angle of depression))
Small: 51 ft*(Tan (41˚)+Tan (4˚))= 47.89 ft
Medium: 83 ft*(Tan (31˚)+Tan (3˚))= 54.22 ft
Large: 69 ft*(Tan (39˚)+Tan (5˚))= 61.91 ft
Volume: Height/3*PI*Radius^2
Small: 47.89/3*PI*0.42^2= 9.04 ft^3
Medium: 54.22/3*PI*0.57^2= 18.47 ft^3
Large: 61.91/3*PI*0.76^2= 37.71 ft^3
Total volume of trees: Calculated volume * number of trees on plot
Small: 9.04 ft^3 * 2= 18.07 ft^3
Medium: 18.47 ft^3 * 5= 92.34 ft^3
Large: 37.71 ft^3 * 3= 113.12 ft^3
Total Volume of all types of trees on plot: 223.53 ft^3
Analysis
The calculations have been made correctly considering the preestablished metrics. In all
approximate calculations there will always be a margin of error which can be reduced by
improvement processes on the measures used, however the calculations made represent the
approximate amount of timber existing on the plot of land measured. It is possible to obtain other
data, such as the approximate distance between each timber providing tree, the amount of space
lost and how much that would affect the purchaser economically and this have more criteria and
information to make a more accurate decision.
Extrapolation:
The estimated total volume of lumber in our sample region was 223.5 cubic feet. To calculate
how many cubic feet of lumber is on each square foot of land, the area’s total region can be
divided by the volume of all trees in the region, resulting in 0.16 ft^3 per ft^2 of land. That figure
can be multiplied by 43,560 to determine how many cubic feet of lumber would be on 1 acre of
land, resulting in roughly 6815 ft^3 of lumber per acre of land. Extrapolating on this figure, 6815
can be multiplied by 23 to determine how many cubic feet of lumber would be on 23 acres of
land. This would result in around 156,744.2 ft^3 of lumber on a 23-acre plot of land.
Conclusion:
The group conclude that when it comes to obtain more effective information about land and
quantities, the best way is to use the mathematics and the necessary formulas to get the desired
answers. By acquired the areas, volumes and heights allowed us to indicate the amount of timber
within a plot of land and to make the decision to invest or not on the plot of land.