Answer:
the resulting error is about 0.754 in²
Step-by-step explanation:
A(r) -A(r0) ≈ dA/dr·(r -r0)
The area of a circle is given by ...
A(r) = πr²
so the derivative is
dA/dr = 2πr
and the area error is ...
dA/dr·(r -r0) = 2π(12 in)(0.01 in) = 0.24π in² ≈ 0.754 in²
