Wetted Bottle Area

There is half a liter of water in the cylinder-shaped bottle. The bottle has an inner diameter of 10 cm. What is the area of the wetted part of the bottle?

Final Answer:

S =  2.7854 dm²

Step-by-step explanation:

$$\begin{gathered} V=0.5\text{l}\to {\text{dm}}^3=0.5\cdot 1{\text{dm}}^3=0.5{\text{dm}}^3 \\ D=10\text{cm}\to \text{dm}=10:10\text{dm}=1\text{dm} \\ r=D/2=1/2=\frac{1}{2}=0.5\text{dm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 0.5^2\doteq 0.7854{\text{dm}}^2 \\ h=V/S_1=0.5/0.7854\doteq 0.6366\text{dm} \\ {S}_2=h\cdot \pi \cdot D=0.6366\cdot 3.1416\cdot 1=2{\text{dm}}^2 \\ S=S_1+S_2=0.7854+2=2.7854{\text{dm}}^2 \end{gathered}$$

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