Radius of a circle is 15 cm and it increases by $3\%$. Find the approximate increase in its area using differentials.
Radius of circle $=r=15$ cm
$\Delta r = 3 \% = 0.03$
Area of circle $=A=\pi r^2$
$\therefore$ $\dfrac{dA}{dr}= 2 \pi r$
$\begin{aligned}
\text{Increase in area} = \Delta A & = \left(\dfrac{dA}{dr}\right) \times \Delta r \\
& = 2 \pi r \times \Delta r \\
& = 2 \times \pi \times 15 \times 0.03 \\
& = 0.9 \pi \;\; cm^2
\end{aligned}$