# 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 =  0.24 m

#### Solution:

$D=1 \ \\ r=D/2=1/2=\dfrac{ 1 }{ 2 }=0.5 \ \\ V=9.42/10=\dfrac{ 471 }{ 500 }=0.942 \ \\ S=\pi \cdot \ r^2=3.1416 \cdot \ 0.5^2 \doteq 0.7854 \ \\ h_{1}=V/S=0.942/0.7854 \doteq 1.1994 \ \\ h=h_{1} \cdot \ 0.20=1.1994 \cdot \ 0.20=0.24 \ \text{m}$

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