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Answer 1 · 2016-07-07T23:58:42

#dot A = 8 (cm^2)/s#

for a cube of side x, the volume is
#V = x^3#

and so differentiating wrt to time, we get #dot V = 3 x^2 dot x quad triangle#

the surface area is #A = 6x^2#

and so differentiating wrt to time again , we get #dot A = 12 x dot x quad square#

we want to know what #dot A # is given a #dot V#, so we connect #dot A# to #dot V# using some simple algebra

from #triangle#, #dot x = (dot V)/(3x^2)#

so from #square#,

#dot A = 12 x (dot V)/(3x^2)#

#dot A = 4 (dot V)/(x)#

#dot A = 4 (20)/(10) = 8 (cm^2)/s#