The surface area  of a cube is  A = , where "a" is the edge measure.


  (a)  the rate of change the surface area of the cube is


            =   cm^2 per second.


       Now substitute given values  a = 3 cm,   = 5 cm per second into the formula and get

            =  =  = 180  cm^2 per second.    ANSWER




  (b)  Solve  it by the same way as (a)

These are related-rates problems.



(a)

The surface area of a cube of side a is:

S =   



The rate of change of surface area, with respect to t, is:

 = 



 = 12a 

 = 5cm/s   (given)



So we can write:

 =  =     (*)



So at a=3cm, the surface area is changing at 

 = 12(3)cm * 5cm/s = 180 





(b) plug a=10cm  into (*)  

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