Q.

If the surface area of a cube is increasing at a rate of 3.6 cm2 /sec, retaining its Shape, rate of change of its volume (in  cm3/sec), when the length of a side of the cube is 10 cm is

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a

10

b

20

c

9

d

18

answer is C.

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Detailed Solution

Let x be the length of the side of the cube  Surface area, s=6x2⇒dsdt=12xdxdt⇒dxdt=3.612×10=0.03 for x=10The rate of change in volume is v=x3⇒dvdt=3x2dxdt=300×0.03=9
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