Finding the Diameter of a Tree
In class, you discovered the relationship between the diameter
and the circumference of a circle or cylinder, and you came up
with a formula like this:
C = d
This equation states that the circumference (C) is equal to the
diameter (d) multiplied by pi (3.14).
What if we know the circumference of the circle but not the
diameter? We know this will change the way our formula looks
like this:
C = d is the same as C = d

1. To find the diameter of the tree, measure the circumference
of the tree four feet from the ground. Use your tape measure to
get accurate measurements from the ground to the four-foot
mark and around the tree. Make sure you and your partner agree
on your measurements!
The circumference of my tree is _____________________
(include units)
2. Calculate the diameter of your tree:
Remember:
C=d

_________________ ÷ pi (3.14) = _____________________
circumference
diameter (include units)
Finding the Crown of a Tree
By measuring the crown of a tree, you will discover another way
that scientists measure the size and health of trees.
1. On your tree, find the longest branches that you can.
2. Stand under the longest branch that has a long branch coming
out of the opposite side of the trunk.
3. Place a string underneath the branch, starting just under the
end of the long branch you have selected, and lay it under the
tree until it is just under the end of the opposite long branch.
Mark the string at that point.
4. Measure the length of the string. This will be the
measurement for the crown of the tree.
______________
(This length is the crown)
5. The crown of my tree is ________________________
(crown measurement with units)
Finding the Height of a Tree
Method 1: Proportional method using a ruler:
1. Have your partner stand at the base of the tree.
2. Back away from the tree, holding your ruler in front of you in a
vertical position. Keep your arm straight. Stop when the tree
and the ruler appear to be the same size. (Close one eye to
help you line it up.)
3. Turn your wrist so that the ruler looks level to the ground and
is in a horizontal position. Keep your arm straight.
4. Have your partner walk to the
spot that you see as the top of
the ruler. Be sure the base of
the ruler is kept at the base of
the tree and your partner is
walking at a 90 degree angle
from your line of sight to the
tree.
5. Measure how many feet he or she walked. That is the tree's
height. Round to the nearest foot and record your answer as
the height.
My tree is _____________________ tall using the ruler
method.
(include units)
6. Switch roles with your partner and repeat Steps 1-5.
If you and your partner obtain completely different results,
measure the height again until you agree on an accurate
measurement.
Method 2: Proportional method using shadows:
1. Measure the length of the shadow of a tree.
2. Measure the length of the shadow of an object of known
height (e.g., the student)
3. Establish an equation representing equivalent proportions
between shadow length and height. Include units.
X ÷ _____________ = _______________ ÷ ___________
(tree height) ÷
(tree shadow length)
=
(student height)
÷
(student shadow length)
4. Solve for tree height (use calculator)
x
= __________ times __________ ÷ _____________
(tree height) = (tree shadow length)
x
(student height)
÷
(student shadow length)
Measured by this method, my tree is ________________tall.
(include units)