I got H for this problem, but I just wanted to confirm that it was the correct answer. If possible, I'd like work shown to compare.

Answer:
you are correct
Step-by-step explanation:
The area of the circle is
A = πr² = π(8 cm)² = 64π cm²
The area of the shaded part is proportional to its central angle, so is ...
(120°/360°)×(64π cm²) = (1/3)·64π cm²