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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 surfacearea of the cube .

This question has multiple parts. Therefore each part has been answered as a separate question on

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:
The surface area of the cube
$ds=12 x dx$
Step 2:
When $x=30,dx \approx \Delta x =0.1$
$\therefore ds=12 \times 30 \times 0.1=36 cm^2$
The maximum error is $ds=36 cm^2$
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