Question

The radius of a puddle is claimed to be 12.0 inches, correct to within 0.01 inch. Use linear approximation to estimate the resulting error, measured in square inches, in the area of the puddle.

Answer 1

I think the answer is 23

Answer 2

the resulting error is about 0.754 in²

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