Q7 of 45 Page 1

The volume of a cube is increasing at the rate of 9 cm3/s. How fast is its surface area increasing when the length of an edge is 10 cm?

Let 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 = x3 and S = 6x2


Also,






Now,


S = 6x2


[using (1)]




Thus, the surface area is increasing at the rate of 3.6 cm2/s.


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