1. **Problem statement:** Find the total area of the shaded regions formed by two concentric circles with radii 3 cm and 6 cm, and a minor sector AOB with angle 60°. 2. **Formula for sector area:** The area of a sector with radius $r$ and angle $\theta$ (in degrees) is given by: $$\text{Area} = \frac{\theta}{360} \times \pi r^2$$ 3. **Calculate area of sector AOB in the larger circle:** $$\text{Area}_{large} = \frac{60}{360} \times \pi \times 6^2 = \frac{1}{6} \times \pi \times 36 = 6\pi$$ 4. **Calculate area of sector AOB in the smaller circle:** $$\text{Area}_{small} = \frac{60}{360} \times \pi \times 3^2 = \frac{1}{6} \times \pi \times 9 = 1.5\pi$$ 5. **Calculate the shaded area:** The shaded area is the difference between the larger sector and the smaller sector: $$\text{Shaded area} = 6\pi - 1.5\pi = 4.5\pi$$ 6. **Final answer:** $$k = 4.5$$ Therefore, the total area of the shaded regions is $4.5\pi$ cm$^2$.