Percentage increase in area

$=\frac {Final \,area - Initial \,area}{Initial \,area} \times 100$

$=\frac{\pi\left(r_2^2-r_1^2\right)}{\pi r_1^2} \times 100$

$=\frac{\left(r_1+\Delta r\right)^2-r_1^2}{r_1^2} \times 100$

where, $\Delta r=$ increase in radius.

$=\left(\frac{r_1^2+2 r_1 \Delta r+\Delta r^2-r_1^2}{r_1^2}\right) \times 100$

$=\frac{2 r_1 \Delta r+\Delta r^2}{r_1^2} \times 100$

As $\Delta r$ is small, we can neglect $\Delta r^2$.

$\approx \frac{2 r_1 \Delta r}{r_1^2}=100$

$=2(\frac{\Delta r}{r_1} \times 100)$

$=2 \times 0.15 \%=0.30 \%$