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 p.i.
pi [(8^2) - (7.8)^2]
8 cm is the radius of the outside of the outer ring, and 7.8 is the radius of the inside of that ring.
I have neglected the bark of the tree when considering the radius of the outer ring to equal (tree diameter)/2
To calculate the area of the outer ring of the cross-section of the tree, we can use the formula for the area of a ring. The formula is:
A = π(r2^2 - r1^2)
Where A is the area, π is the approximation of pi (3.14), r2 is the radius of the outer ring, and r1 is the radius of the inner ring.
In this case, we are given that the diameter of the tree is 16 centimeters. The radius of the outer ring is half of the diameter, so it would be 8 centimeters. The width of the outer ring is given as 2 centimeters, which means the radius of the inner ring would be 8 - 2 = 6 centimeters.
Now we can substitute the values into the formula:
A = 3.14((8^2) - (6^2))
Simplifying the equation:
A = 3.14(64 - 36)
A = 3.14(28)
A ≈ 87.92
So, the area of the outer ring of the cross-section of the tree is approximately 87.92 square centimeters.