Answer
$16.7$ $cm^{2}$
Work Step by Step
$A$ = $x^{2}+\frac{1}{2}{\pi}\left(\frac{1}{2}x\right)^{2}$ = $\left(1+\frac{\pi}{8}\right)x^{2}$
$dA$ = $\left(2+\frac{\pi}{4}\right)xdx$
When $x$ = $60$
and $dx$ = $0.1$
$dA$ = $\left(2+\frac{\pi}{4}\right)(60)(0.1)$ = $12+\frac{3\pi}{2}$
so the maximum error is approximately
$12+\frac{3\pi}{2}$ $\approx$ $16.7$ $cm^{2}$
