Browse Questions

# The radius of a circular disc is given as $24cm$ with a maximum error in mesurement of $0.02cm$ compute the relative error?

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
• $\large\frac{\Delta y}{y}=\frac{Actaual\;change\;in \;y}{Actual\;value\;of \;y}$$=relative \;error • \large\frac{\Delta y}{y}$$ \times 100 =percentage\; error$
The relative error in area is $\large\frac{\Delta A}{A}=\frac{0.96 \pi}{\pi \times 24}$
$\qquad=\large\frac{0.04}{24}$
$\qquad=\large\frac{0.01}{6}$
$\qquad=0.001667$