$8$:$15$ C

$-$Il $96$

Photo

Done

Q$3.$ The volume of a right truncated cone of height $h$ and radii $R$ and $r$ is given by the equation:

$V=\frac{h}{3}(R^2+Rr+r^2)$

$($a$)$ Use first order approximations to estimate the error in V given that:

$R=(10+-0\mathrm{.}1)cm,r=(5+-0\mathrm{.}2)cm,h=9+-0\mathrm{.}3cm$

$[$Note: $[$:$,V_{\text{a}\text{p}\text{p}}=|\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{R}}|R+|\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{r}}|r+|\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{h}}|h\}$

$($b$)$ Using the extremity values of $R,r$ and h $,$ compute the true error $V_{\text{t}\text{r}\text{u}\text{e}}$ in V $.$

$($c$)$ Find the true relative percentage error.