Lời giải 

\( S = \int_{-2}^{2} \left( 4 - x^2 \right) \, dx = \frac{32}{3}\)

Tìm \( c \) nào cho:   \( \int_{-\sqrt{c}}^{\sqrt{c}} \left( c - x^2 \right) \, dx = \frac{16}{3}, \quad c \in (0, 4) \)

\( \Rightarrow c x - \frac{x^3}{3} \bigg|_{-\sqrt{c}}^{\sqrt{c}} = \frac{4}{3} c \sqrt{c} = \frac{16}{3}. \Rightarrow c \sqrt{c} = 4\)

\(\Rightarrow c^\frac{3}{2} = 4 \Rightarrow c^3 = 16 \quad \Rightarrow c = \sqrt[3]{16} \)

\(\Rightarrow\) Vậy chọn đáp án \(\boxed{\text{A}} \)