If side length of cube changing at `0.1mm//sec`. Then what will be rate of change of volume, when side length is 2 meter

Options

A. `8xx10^(-4)m^(3)//sec`
B. `4xx10^(-3)m^(3)//sec`
C. `12xx10^(-4)m^(3)//sec`
D. `12xx10^(-3)m^(3)//sec`

Answer

C

Explanation

`v=l^(3)`
`(dv)/(dt)=3l^(2)((dl)/(dt))`
`((dv)/(dt))=3(2)^(2)(10^(-4)m^(3)//sec)`
`((dv)/(dt))=12xx10^(-4)m//sec`