Answer
$2\sqrt {3}\,cm/s $
Work Step by Step
Let the diagonal of the cube be $ r $ and its edge be $ a $.
We are given that $\frac{da}{dt}=2\,cm/s $
The length of the diagonal of a cube with edge length equal to $ a $ is $\sqrt {3}a $.
That is, $ r=\sqrt {3}a $
$\frac{dr}{dt}=\frac{dr}{da}\times\frac{da}{dt}=\frac{d}{da}(\sqrt {3}a)\times2\,cm/s $
$=2\sqrt {3}\,cm/s $
