A) \[750\text{ }c{{m}^{3}}/s\]
B) \[75\,c{{m}^{3}}/s\]
C) \[300\text{ }c{{m}^{3}}/s\]
D) \[150\,\,c{{m}^{3}}/s\]
E) \[25c{{m}^{3}}/s\]
Correct Answer: A
Solution :
Let a be the edge of cube. Then, \[\frac{da}{dt}=10\,cm/s\] (Given) ...(i) \[\because \]Volume of cube is \[V={{a}^{3}}c{{m}^{3}}\] \[\Rightarrow \] \[\frac{dV}{dt}=3{{a}^{2}}\frac{da}{dt}c{{m}^{3}}/s\] \[=3\times {{5}^{2}}\times 10c{{m}^{3}}/s\] [using Eq. (i)] \[=750\,c{{m}^{3}}/s\]
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