A sector of a circle of radius 4 cm contains an angle of 30°.

We know that the area A of a sector of an angle θ in the circle of radius r is given by

$A=\frac{\theta}{360^{\circ}} \times \pi r^{2}$

It is given that $r=4 \mathrm{~cm}$ and angle $\theta=30^{\circ}$.

Now we substitute the value of r and θ in above formula,

$A=\frac{30^{\circ}}{360^{\circ}} \times \pi \times 4 \times 4 \mathrm{~cm}^{2}$

$=\frac{4 \pi}{3} \mathrm{~cm}^{2}$