1. **State the problem:** We need to find the area of the shaded sector of a circle with radius 16 inches and central angle 150°. 2. **Formula for the area of a sector:** The area $A$ of a sector with radius $r$ and central angle $\theta$ (in degrees) is given by: $$A = \pi r^2 \times \frac{\theta}{360}$$ 3. **Apply the values:** Here, $r = 16$ inches and $\theta = 150^\circ$. $$A = \pi \times 16^2 \times \frac{150}{360}$$ 4. **Simplify the fraction:** $$\frac{150}{360} = \frac{5}{12}$$ 5. **Final expression:** $$A = \pi \times 16^2 \times \frac{5}{12}$$ 6. **Explanation:** The area of the sector is a fraction of the full circle's area $\pi r^2$, proportional to the ratio of the central angle to the full angle $360^\circ$. **Answer:** The correct expression is option B: $\pi(16^2)\frac{150}{360}$.