# 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).

Result

h =  0.24 m

#### Solution:

$D = 1 \ \\ r = D/2 = 1/2 = \dfrac{ 1 }{ 2 } = 0.5 \ \\ V = 9.42/10 = \dfrac{ 471 }{ 500 } = 0.942 \ \\ S = \pi \cdot \ r^2 = 3.1416 \cdot \ 0.5^2 \doteq 0.7854 \ \\ h_{ 1 } = V/S = 0.942/0.7854 \doteq 1.1994 \ \\ h = h_{ 1 } \cdot \ 0.20 = 1.1994 \cdot \ 0.20 \doteq 0.2399 = 0.24 \ \text{ m }$

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