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Q.

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

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a

10

b

20

c

18

d

9

answer is D.

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Detailed Solution

Let the side of cube be ‘a’
 s=6a2⇒dsdt=12adadt ⇒3⋅6=12a⋅dadt
12(10)⋅dadt=3.6⇒dadt=0.03 V=a3 ⇒dvdt=3a2dadt=3(10)2⋅3100=9

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