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If the surface area of a cube is increasing at a rate of 3.6\; cm^{2}/sec, retaining its shape ; then the rate of change of its volume (in cm^{2}/sec) , when the length of a side of the cube is 10\; cm, is :
Option: 1 18
Option: 2 10
Option: 3 20
Option: 4 9

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\\ \frac{d}{d t}\left(6 a^{2}\right)=3.6 \Rightarrow 12 a \frac{d a}{d t}=3.6 \\ \text { a } \frac{d a}{d t}=0.3 \\ \frac{d v}{d t}=\frac{d}{d t}\left(a^{3}\right)=3 a\left(a \frac{d a}{d t}\right) \\ =3 \times 10 \times 0.3=9

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