# 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 .

This question has multiple parts. Therefore each part has been answered as a separate question on Clay6.com

Toolbox:
• 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 $v=x^3$
$dv=3x^2dx$
Step 2:
When $x=30,dx \approx \Delta x=0.1$
$\qquad dv=3 \times 900 \times 0.1$
$\qquad\quad=270$
The maximum error is $dv=270 cm^3$