Two cylinders

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

Correct answer:

t =  1.3464 s

Step-by-step explanation:

$$\begin{gathered} r=1\text{cm} \\ h=3\text{cm} \\ S=\pi \cdot r^2=3.1416\cdot 1^2\doteq 3.1416{\text{cm}}^2 \\ V=S\cdot h=3.1416\cdot 3\doteq 9.4248{\text{cm}}^3 \\ {s}_1=9{\text{cm}}^3\text{/s} \\ 1ml=1c{m}^3 \\ {s}_2=2{\text{cm}}^3\text{/s} \\ t=\frac{V}{s_1-s_2}=\frac{9.4248}{9-2}=1.3464\text{s} \end{gathered}$$

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