Question

You can estimate a tree's age in years by using the formula a = r w , where r is the tree's radius without bark and w is the average thickness of the tree's rings. the circumference of a white oak tree is 90 inches. the bark is 0.5 in. thick, and the average thickness of a ring is 0.2 in. estimate the tree's age and the area enclosed by the outer circumference of the widest ring.

Answer 1

Circumference of a white oak tree:
C = 90 in.
C = 2 r π
2 r π = 90
r · 6.28 = 90
r = 90 : 6.28
r = 14.33 in ( but it is not r in the formula )
Since the bark is 0.5 in thick: r = 14.33 - 0.5 = 13.83 in
a = r : w = 13.83 : 0.2 = 69.15 years
The widest ring is one that shows 69 years:
r = 69 · 0.2 = 13.8 in
A = r² π = 13.8² · 3.14 = 190.44 · 3.14 = 597.98 in²
Answer: The tree`s age is 69.15 years ( or 69 years and 2 months ) and the area enclosed by the  outer circumference of the widest ring is 597.98 in².