Answer
change in diameter = $\frac{2}{\pi}$
change in cross section = $10\ in^2$
Work Step by Step
The given change in circumference of a tree: (dC)=2
We need to find the change in diameter (dD)
circumference(c)=$\pi d$
change in circumference $(dC)=\pi dD$
so $2=\pi dD$
and $dD=\frac{2}{\pi}$
change in cross-sectional area, diameter(D)=10in.
area(A)=$\pi r^2=\pi {\frac{D^2}{4}}$
change in cross section (dA) = $\frac{2\pi}{4}DdD=\frac{2\pi\times2\times10}{4\pi}=10in^2$
Thus, the final answer is:
change in diameter = $\frac{2}{\pi}$
change in cross section = $10\ in^2$
