Chapter 11.3, Problem 31PPS

a.

To determine

The diameter of the tree with a given circumference.

Answer to Problem 31PPS

The diameter of the tree is 0.8 ft (approx.).

Explanation of Solution

Given: The circumference of the tree is 2.5 ft.

Concept Used: The circumference C of any circle with diameter d is given by-

  $C=\pi d$ .

Calculations: The circumference of the given tree is 2.5ft. Let its diameter be d. Then,

  $2.5=\pi d$

  $\Rightarrow d=\frac{2.5}{\pi }$

  $\Rightarrow d=\frac{2.5}{3.14}$

  $\Rightarrow d=0.796$

  $\Rightarrow d\approx 0.8$

Thus, the diameter of the given tree is 0.8 ft (approx.).

b.

To determine

The age of the tree.

Answer to Problem 31PPS

The age of the given tree is 3.6 years.

Explanation of Solution

Given: The diameter of the tree is 0.8 ft and its growth factor is 4.5.

Concept Used: The age of a tree can be determined by multiplying the diameter of a tree to its growth factor.

Calculations: The age of the tree whose diameter is 0.8ft and has a growth factor 4.5 will be-

Age $=0.8\times 4.5$ years

  $=3.6$ years

Thus, the age of the tree is 3.6 years.