Early in his career, Andrew Ellicott Douglass (1867-1962) noticed a connection between climate and the growth of plants. Studying this connection, Douglass was able to develop the science of dendochronology, a method for dating events and climate variations by studying the growth rings of trees and ancient wood.
The concentric circles, or growth rings, represent the cross-section of a tree with a diameter of 16 centimeters. The width of the outer tree ring measures 2 centimeters. What is the area in square centimeters of the outer ring of the cross-section of the tree? Use 3.14 for .
The entire area of the tree is PI*16^2
The area inside the ring is PI*14^2
The difference is the area of the ring.
114 cm.
area of outer circle A1=Pi*16^2= 803.84
area of inner circle A2=Pi*14^2= 615.44
area of outer ring=A1-A2=188.4 cm
87.92 cm2 =D
To find the area of the outer ring of the cross-section of the tree, we need to subtract the area of the inner circle (formed by the inner ring) from the area of the outer circle (formed by the outer ring).
1. Find the radius of the outer circle:
The diameter of the tree cross-section is given as 16 centimeters, which means the radius (r) is half of that, i.e., 16/2 = 8 centimeters.
2. Find the area of the outer circle:
The formula to calculate the area of a circle is A = π*r^2, where A is the area and π is approximately 3.14.
Substituting the values, the area of the outer circle is A = 3.14 * (8)^2 = 3.14 * 64 = 200.96 square centimeters.
3. Find the radius of the inner circle:
The width of the outer tree ring is given as 2 centimeters. Since the width is the difference between the two radii, the radius of the inner circle would be 8 - 2 = 6 centimeters.
4. Find the area of the inner circle:
Using the same formula as before, the area of the inner circle is A = 3.14 * (6)^2 = 3.14 * 36 = 113.04 square centimeters.
5. Find the area of the outer ring:
Subtract the area of the inner circle from the area of the outer circle:
Area of outer ring = Area of outer circle - Area of inner circle
= 200.96 - 113.04
= 87.92 square centimeters.
Therefore, the area of the outer ring of the cross-section of the tree is 87.92 square centimeters.