Answer
(a) The maximum error is $30.16~cm^2$
(b) The relative error is $0.0167$
The percentage error is $1.67\%$
Work Step by Step
(a) Let $r$ be the radius.
$r = 24~cm$
$dr = 0.2~cm$
We can find the maximum possible error:
$A = \pi ~r^2$
$dA = 2\pi ~r~dr$
$dA = (2\pi)(24~cm)~(0.2~cm)$
$dA = 30.16~cm^2$
(b) We can find the relative error:
$\frac{dA}{A} = \frac{2\pi~r~dr}{\pi~r^2} = 2~(\frac{dr}{r})$
$\frac{dA}{A} = 2~(\frac{0.2~cm}{24~cm})$
$\frac{dA}{A} = 0.0167$
The percentage error is $1.67\%$
