Vintner

How high can vintner fill keg with crushed red grapes if these grapes occupy a volume of 20 percent? Keg is cylindrical with a diameter of the base 1 m and a volume 9.42 hl. Start from the premise that says that fermentation will fill the keg (the number П equals 3.14).

Correct result:

h =  0.2399 m

Solution:

$$\begin{gathered} D=1 \\ r=D\mathrm{/}2=1\mathrm{/}2={\displaystyle \frac{1}{2}}=0.5 \\ V=9.42\mathrm{/}10={\displaystyle \frac{471}{500}}=0.942 \\ S=\pi \cdot r^2=3.1416\cdot 0.5^2\doteq 0.7854 \\ {h}_1=V\mathrm{/}S=0.942\mathrm{/}0.7854\doteq 1.1994 \\ h=h_1\cdot 0.20=1.1994\cdot 0.20=0.2399\text{ m} \end{gathered}$$

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