Let's call the side length of the cube 'x'
We are given: dV/dt = 23 & we seek to find: dA/dt
Generally what I do is express the Surface Area(A), Volume(V) in terms of 'x'
So A=6x^2 and V=x^3
To find dA/dt we need to somehow incorporate dV/dt via chain rule.
The way we can do that is by using the aforementioned expressions for surface area and volume.
dA/dt = (dA/dx) x (dx/dV) x (dV/dt) (Notice how I set my chains up so that the dx's and dV's will cancel. It takes practice, but it's very simple once you get your head around a few similar types of problems.)
dA/dt = (12x) x (1/3x^2) x 23 = 92/x
When x=140, dA/dt = 23/35 mm^2/second (Be careful of the units! Fortunately, everything is in mm so no conversion is needed)