If an error of $1^{\circ}$ is made in measuring the angle of a sector of radius $30 \mathrm{~cm}$, then the approximate error in its area, is

$25 \pi \mathrm{cm}^2$

Let A be the area and $\theta$ (in radians) be the sector angle. Then,

$A=\frac{1}{2} \times 30^2 \times \theta=450 ~\theta$          $\left[∵ A=\frac{1}{2} r^2 \theta\right]$

$\Rightarrow \frac{d A}{d \theta}=450$

Let $\Delta \theta$ be an error in $\theta$ and $\Delta A$ be the corresponding error in $A$. Then,

$\Delta A=\frac{d A}{d \theta} \Delta \theta$

$\Rightarrow \Delta A=450 \times \frac{\pi}{180}$            $\left[∵ \Delta \theta=1^{\circ}=\frac{\pi}{180}\right.$ radians $]$

$\Rightarrow \Delta A=2.5 \pi \mathrm{cm}^2$