Q. 2 4.4( 49 Votes )

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?

Answer :

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,


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 .

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