Molecular Theory & Factors question from MHT CET 2021 (23 Sep, Shift 2)

Answer: (a)

1. Volume is conserved: $\frac{4}{3}\pi r^3 = 1\text{ cm}^3 \Rightarrow r = \left(\frac{3}{4\pi}\right)^{1/3}$.
2. Area $A = 4\pi r^2 = 4\pi\left(\frac{3}{4\pi}\right)^{2/3} = \left(64\pi^3 \cdot \frac{9}{16\pi^2}\right)^{1/3}$.
3. $A = (36\pi)^{1/3}\text{ cm}^2$. So the answer is (a).