Question

The radius of a circle is estimated to be
14 inches, with a maximum error in measure-
ment of ±0.08 inches. Use differentials to
estimate the maximum error in calculating
the area of the circle using this estimate.

Answer 1

\[A= \pi r^2\]

Answer 2

\[\frac{dA}{dr} = 2 \pi r \]

Answer 3

sub in r=0.08

Answer 4

\[|\epsilon| \le 2(.08)\pi = 1.6\pi \]

Answer 5

in inches (whatever unit you measured the radius with).