The volume of a cube is increasing at a rate of `7c m^3//s ec` How fast is the surface area increasing when the length of an edge is 12cm?

Explanation

Let us take that x be the length of an edge of the cube

V be the volume

and S be the surface area at any time t.

Then, `V=x^3` and `S=6x^2`.
Given `(dV)/dt`=`7c m^3//s ec`

=`d/(dt)(x^3)=7`

`=>3x^2(dx/dt)=7`

`=>dx/dt=7/(3x^2)`

Now, `S=6x^2`

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