The volume of a cube is increasing at the rate of 8 cm³/s. How fast is the surface area increasing when the length of an edge is 12 cm?

Let a be the length of a side, V be the volume and S be the surface area of the cube.

Then, V = a³ and S = 6a² where a is the function of time t.

Now, It is given that

Then, by using the chain rule, we get,

………………(1)

So, when a = 12cm, then,

Therefore, if the length of the edge of the cube is 12cm, then the surface area is increasing at the rate of .