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प्रश्न
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 metre per second. In how much time the tank will be filled?
उत्तर
Radius of the cylindrical tank = 0 . 7 m
Height of the cylindrical tank = 2 . 1 m
\[\text{ Volume of the cylindrical tank }= \pi(0 . 7 )^2 (2 . 1) m^3 \]
Length of the water column flown from the pipe in 1 s = 2 m
Let the time taken to completely fill the water tank be x sec.
Length of the water column flown from the pipe in x sec = 2 x m
Radius of the pipe = 1 . 75 cm = 0 . 0175 m
\[\text{ Volume of the water column flown from the pipe in x }\sec = \pi(0 . 0175 )^2 (2 x) m^3 \]
\[\text{ Volume of the cylindrical tank }=\text{ Volume of the water column flown from the pipe }\]
\[\pi(0 . 7 )^2 (2 . 1) = \pi(0 . 0175 )^2 (2 x)\]
\[x = \frac{0 . 7 )^2 (2 . 1)}{0 . 0175 )^2 (2 )} = 1680 \sec = 28 \min\]
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