# Propagation of Error on Radius of a Circle

I need to calculate the radius of a circle and its error from the chord length $L$ and height $h$ from the chord to the circumference of the circle.

I know the formula for $R$ to be $R = \frac{4h^2+L^2}{8h}$. Using the standard propagation of error formula ${\sigma_Z}^2 = ({\delta Z \over \delta A})^2 {\sigma_A}^2 + ({\delta Z \over \delta B})^2 {\sigma_B}^2$, I tried to calculate R and its error, but my answer and the book's answer are pretty off.

The values for $L$ and $h$ respectively are $(125.0\pm 5.0)cm$, $(0.51\pm 0.22) cm$.

What I did was,

$\sigma_R^2 = \sigma_h^2(0.5 - \frac{L^2}{8h^2})^2 + \sigma_L^2 (\frac{L}{4h})^2$.

My error however turns out to be "only" $\backsim 1700$, whereas the book is listing the error as $\backsim 6700$.

Here is my wolfram alpha calculation.

Can anyone help? My instructor said the book provided the wrong $R$ formula originally, so we corrected it, but even after correcting it my error is still pretty far from theirs.

• Is the book's answer the answer you would get using its incorrect formula? – Adrian Feb 3 '15 at 4:35
• No, it isn't, I did try both. I don't know how they got that answer. – A4Treok Feb 3 '15 at 4:37
• Your calculation seems to be correct from what I can tell. Their answer is off by almost a factor of four, which could be a clue. – Adrian Feb 3 '15 at 4:54
• Yeah, I mean, this should be pretty simple. Not sure how they got their result, but this book has a ton of errors. Thanks for your help. – A4Treok Feb 3 '15 at 4:57