A cylindrical water tank of diameter $1.4 m$ and height $2.1 m$ is being fed by a pipe of diameter $3.5 c m$ through which water flows at the rate of $2 m / s$ . Calculate the time, it takes to fill the tank.

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Solution

given, water tank:
$d i a m e t e r = 1.4 m ⟹ r a d i u s (r_{1}) = \frac{1.4}{2} = 0.7 m = 70 c m$ and
$h e i g h t (h_{1}) = 2.1 m = 210 c m$
and pipe:
$d i a m e t e r = 3.5 c m ⟹ r a d i u s (r_{2}) = \frac{3.5}{2} = \frac{7}{4} c m$ and
rate of flow = 2 m/s =200 cm/s
time taken by the pipe to fill the tank = $\frac{volume of cylindrical water tank}{volume of the pipe}$ $= \frac{π r_{1}^{2} h_{1}}{π r_{2}^{2} h_{2}}$
(since, volume of cylinder = $π r^{2} h$ )
on substituting,
$⟹ time taken = \frac{π \times 70 \times 70 \times 210}{π \times \frac{7}{4} \times \frac{7}{4} \times 200}$
$= 1680 s e c = \frac{1680}{60} m i n = 28 m i n$
therefore, time taken to fill the tank $= 28$ minutes

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A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 m/s. Calculate the time, it takes to fill the tank.

A cylindrical water tank of diameter $1.4 m$ and height $2.1 m$ is being fed by a pipe of diameter $3.5 c m$ through which water flows at the rate of $2 m / s$ . Calculate the time, it takes to fill the tank.