Glass Waste Container Hole

The round hole of the glass waste container has a diameter of 18 cm. Will a four-liter glass pass through this hole? If there are 4 liters of water in the glass, it reaches a height of 20 cm.

Result

x=

Yes

No

Step-by-step explanation:

$$\begin{gathered} D_1=18\text{cm} \\ {r}_1=D_1/2=18/2=9\text{cm} \\ V=4\text{l}\to {\text{cm}}^3=4\cdot 1000{\text{cm}}^3=4000{\text{cm}}^3 \\ h=20\text{cm} \\ V=S\cdot h \\ S=V/h=4000/20=200{\text{cm}}^2 \\ S=\pi r_2^2 \\ {r}_2=\sqrt{S/\pi }=\sqrt{200/3.1416}\doteq 7.9788\text{cm} \\ x=r_2<r_1=7.9788<9=1 \end{gathered}$$

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