Real-Life Math
Being an arborist in one of the world's most famous botanical
gardens, you are expected to take good care of the trees and woody plants
that attract tourists from around the world. With thousands of people walking
through the garden every day, you are responsible for preventing trees from
tipping over and endangering the workers and tourists. You will have to use
math to do this.
Your biggest enemies are diseases and insects that
claim the lives of your trees. Although a tree may have been affected by a
disease or devoured by hungry insects, it may appear sturdy.
So what
can you do to figure out what trees might endanger your visitors? Believe
it or not, your most powerful tool is actually your math. "Arithmetic is always
in demand for simple calculations," says arborist Julian Dunster. "Basic math
is essential."
In this case, calculations and measurements
need to be made to keep weak trees from unexpectedly tipping over one day.
To determine whether a tree is safe, you compare the required shell thickness
(RST) to actual shell thickness (AST). The procedure is as follows:
Steps
- First, you measure the diameter at stump height (DSH) at 30 cm above ground
level (measure on the high side if the ground is sloped). This measurement
is made outside the bark.
- Divide diameter inside the bark by 2 to determine radius.
- Multiply the radius by 0.3 to determine required shell thickness (RST).
The RST is 30 percent of the tree radius.
- Bore tree at stump height (2 or more borings may be required) to determine
actual shell thickness (AST).
- Compare RST with AST. If the AST is equal to or greater than the RST,
the stemwood condition is considered safe (S). If the AST is less than the
RST, the stemwood condition is dangerous (D).
You have 2 trees to test. You know from your measurements that the
diameter (DSH) of 1 tree is 70 cm. You also know that the AST of that tree
is 9 cm.
The other tree has a DSH of 32 cm and an AST of 10 cm.
Based
on this information, can you calculate whether these 2 trees are dangerous?