2011-I-13

$\begin{array}{rcl}\pi R^2\times {\displaystyle \frac{{288}^{\circ }}{{360}^{\circ }}}& =& 2880\pi \\ R^2& =& 3600\\ R& =& 60\end{array}$

所以，$OX$ 的長度為 $60\text{ mm}$。

$\begin{array}{rcl}\pi \times r\times 60& =& 2880\pi \\ r& =& 48\end{array}$

所以，該容器的高度

$\begin{array}{cl}=& \sqrt{{60}^2–{48}^2}\\ =& 36\text{ mm}\end{array}$

$\begin{array}{cl}=& {\displaystyle \frac{1}{3}}\pi \times (48{)}^2\times 36\\ =& 86858.75369{\text{ mm}}^3\\ =& 86.85875369{\text{ cm}}^3\\ <& 150{\text{ cm}}^3\end{array}$

所以，水會溢出。