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The edge of a cube was found to be $30cm$ with a possible error in mesurement of $ 0.1cm$. Use differentials to estimate the maximum possible error in computing the volume of the cube .

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1 Answer

  • Let $y=f(x)$ be a differentiable function then the quantities $dx$ and $dy$ are called differentials.The differential $dx$ is an independent variable.
  • The differential $dy$ is then defined by $dy=f'(x)dx(dx \approx \Delta x)$
  • Also $f(x+\Delta x)-f(x)=\Delta y =dy $ from which $f(x+\Delta x) $can be evaluated
Step 1:
Let x be the side of the cube of the volume $v=x^3$
Step 2:
When $x=30,dx \approx \Delta x=0.1$
$\qquad dv=3 \times 900 \times 0.1$
The maximum error is $dv=270 cm^3$
answered Aug 12, 2013 by meena.p

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