Glass of juice

A cylindrical glass 13 cm tall with a base diameter of 9 cm is filled with juice to a level 3 cm below the rim. Determine the maximum angle to which the glass can be tilted without the juice spilling.

Final Answer:

α =  33.7 °

Step-by-step explanation:

$$\begin{gathered} h=13\text{cm} \\ d=9\text{cm} \\ x=3\text{cm} \\ r=d/2=9/2=\frac{9}{2}=4.5\text{cm} \\ t=\tan \alpha =x:r \\ t=\frac{x}{r}=\frac{3}{4.5}=\frac{2}{3}\doteq 0.6667 \\ \alpha =\frac{180°}{\pi }\cdot \arctan t=\frac{180°}{\pi }\cdot \arctan 0.6667=33.7^{\circ }=33°41^{\prime }24" \end{gathered}$$

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