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Question 2:
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 x be the length of a side, V be the volume, and s be the surface area of the cube.
Then, V = x3 and S = 6x2 where x is a function of time t.
It is given that
.
Then, by using the chain rule, we have:
∴
⇒
Thus, when x = 12 cm, 
Hence, if the length of the edge of the cube is 12 cm, then the surface area is increasing at the rate of
cm2/s.
