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प्रश्न
Water flows through a cylindrical pipe , whose inner radius is 1 cm , at the rate of 80 cm /sec in an empty cylindrical tank , the radius of whose base is 40 cm . What is the rise of water level in tank in half an hour ?
उत्तर
The inner radius of the cylindrical pipe r =1 cm.
Rate of flow of water = 80 cm/sec
volume of the water that flows through pipe in 1sec is
\[\pi r^2 \times 80 = 80\pi {cm}^3\]
volume of the water that flows through pipe in half an hour
\[80\pi \times 30 \times 60 = 144000\pi {cm}^3\]
radius of the base of the cylindrical tank is R = 40 cm
let the water level in the cylinderical tank after half an hour be h.
volume of the raised water = \[\pi \left( R \right)^2 h = \pi \left( 40 \right)^2 h\]
volume of the raised water in tank = volume of the water that flows through pipe
\[\Rightarrow \pi \left( 40 \right)^2 h = 144000\pi\]
\[ \Rightarrow h = \frac{144000}{1600} = 90 cm\]
Thus water level will rise by 90 cm in half an hour.
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