## Thomas' Calculus 13th Edition

$$\approx 1.625 \%$$
Re-write as: $dA=\pi \ b \ da+\pi a \ db$ $dA(10,16)=16\pi \ da+10\pi db$ Set $da=\pm 0.1 \\ db=\pm 0.1$ $\implies dA=\pm 26(\pi) (0.1)=\pm 2.6 \pi$ The estimated change in $A$ can be computed as $dA=|\dfrac{dA}{A} \times 100|=|\dfrac{2.6 \pi}{160 \ \pi} \times 100 | \approx 1.625 \%$