Trying to understand this. Problem states "The radius of a circular disk is given as 24cm with a maximum error of 0.2cm. An estimate, via linearisation, of the maximum error in the calculated area of the disk is ?

This is what I have done and think it's right.

$\displaystyle

\begin{array}{l}

A = \pi r^2 \\

A'(r) = 2\pi r \\

\Delta r = 0.2 \times r = 0.2r \\

\Delta A = A'(r) \times \Delta r = 2\pi r \times 0.2r = 0.4\pi r^2 = 0.4A \\

\end{array}

$

The answer is given as being $\displaystyle 9.6\pi {\rm cm}^2 $

But I would have thought it to be $\displaystyle r^2 \pi \times 0.4 = 0.4 \times (24)^2 \pi = 576 \times 0.4\pi = 230.4\pi$

Am I completely out of my mind? What am I not getting here?