\[\begin{array}{1 1}(1)8cm^{2}/sec&(2)16cm^{2}/sec\\(3)2cm^{2}/sec&(4)4cm^{2}/sec\end{array}\]

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Let V be the volume ad a be the side of the cube for time 't' Volume of the cube. $V= a^2$

Given $\large\frac{dV}{dt}$$=4 \;cm^2 sec $

$V= 8\;cm^2$

When $V=g => a^3 =8=2^3$

$a=2\;cm$

$S= 6a^2$

$V= a^3$

$\large\frac{dV}{dt} $$=3a^2. \large\frac{da}{dt}$

$4=3a^2 \large\frac{da}{dt}$

$\large\frac{4}{3a^2} =\frac{da}{dt}$

$S= 6a^2$

$\large\frac{dS}{dt} $$=12 a \large\frac{da}{dt}$

$\quad= 12 a \times \large\frac{4}{3a^2}$

$\large\frac{dS}{dt}=\frac{16}{a}$

$\qquad= \large\frac{16}{2}$

$\qquad= 8 \;cm^2 sec$

Hence 1 is the correct answer.

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