If the side of a cube decreases by 1%,the vol | vedclass

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(D) Let the side of the cube be $L$. The volume of the cube is $V = L^3$.Taking the derivative,the change in volume is given by $\Delta V = 3L^2 \Delt

Vedclass · Accepted Answer

$3$

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(D) Let the side of the cube be $L$. The volume of the cube is $V = L^3$.Taking the derivative,the change in volume is given by $\Delta V = 3L^2 \Delta L$.The fractional change in volume (volume strain) is $\frac{\Delta V}{V} = \frac{3L^2 \Delta L}{L^3} = 3 \frac{\Delta L}{L}$.Given that the side decreases by $1\%$,we have $\frac{\Delta L}{L} = 1\% = 0.01$.Therefore,the volume strain is $3 	imes 1\% = 3\%$.Thus,the volume strain is $3\%$.

If the side of a cube decreases by $1\%$,the volume strain is ........ $\%$.

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