[填空题]
The volume $V$ of a cone of height $h$ and radius $r$ is given by the expression: $$V=\frac{\pi r^2 h}{3}$$ In a particular experiment, there is a $5.0 \% $ uncertainty in $V$ and a $2.0 \%$ uncertainty in $r$. What is the percentage uncertainty in $h$ ? % (Remember to exclude the $\%$ symbol with your answer)
参考答案: 9.0
本题详细解析: Rearranging the equac(b1zc wxc . )ev0fis(tion gives: $$ h=\frac{3 V}{\pi r^2} $$ Combining the uncertainty when dividing or multiplying requires you to add the percentage uncertainties. In this case, we must add the percentage uncertainties of $\mathrm{V}, \mathrm{r}$ and $\mathrm{r}$ ( $\mathrm{r}$ twice because it is squared): so the percentage uncertainty in $h$ is $(5 \%+2 \times 2 \%)=9 \%$.
