# Two cylinders

Two cylinders are there one with oil and one with an empty oil cylinder has no fixed value assume infinitely. We are pumping out the oil into an empty cylinder having radius =1 cm height=3 cm rate of pumping oil is 9 cubic centimeters per sec and we are pumping out oil from an empty cylinder with a rate of 2 millimeters per sec. Find the time to make the oil cylinder having radius=1 empty

Result

t =  1.346 s

#### Solution:

$r = 1 \ cm \ \\ h = 3 \ cm \ \\ \ \\ S = \pi \cdot \ r ^2 = 3.1416 \cdot \ 1 ^2 \doteq 3.1416 \ cm^2 \ \\ \ \\ V = S \cdot \ h = 3.1416 \cdot \ 3 \doteq 9.4248 \ cm^3 \ \\ \ \\ s_{ 1 } = 9 \ cm^3/s \ \\ 1 \ ml = 1 \ cm^3 \ \\ \ \\ s_{ 2 } = 2 \ cm^3/s \ \\ \ \\ t = \dfrac{ V }{ s_{ 1 }-s_{ 2 } } = \dfrac{ 9.4248 }{ 9-2 } \doteq 1.3464 = 1.346 \ \text { s }$

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