Answer
$\frac{dS}{dt}=\frac{4}{3}$ $\frac{cm^2}{min}$
Work Step by Step
Let suppose, the edge length $=x$, then $V=x^3$
Differentiate on both sides;
$\frac{dV}{dt}=3x^2\frac{dx}{dt}$
$3x^2\frac{dx}{dt}=10$
$\frac{dx}{dt}=\frac{10}{3x^2}$
And,
$S=6x^2$
$dS=12x\frac{dx}{dt}$
putting value of $\frac{dx}{dt}$.
$=12x(\frac{10}{3x^2})$
$=\frac{120x}{3x^2}$
$=\frac{40}{x}$
when $x=30$, we get,
$\frac{dS}{dt}=\frac{40}{30}$
$\frac{dS}{dt}=\frac{4}{3}$
hence,
$\frac{dS}{dt}=\frac{4}{3}$ $\frac{cm^2}{min}$
