Question

# A cylindrical pipe has inner diameter of $$4$$ cm and water flows through it at the rate of $$20$$ per minute. How long would it take to fill a conical tank of radius $$40$$ cm and depth $$72$$ cm?

Solution

## We haveDiameter of base of conical vessel $$=80cm$$so, radius $$=40cm$$and, Height of the conical vessel $$72cm$$Thus volume of conical vessels $$= \pi {r^2}\dfrac{h}{3}$$$$= \pi \times {\left( {40} \right)^2} \times \dfrac{{72}}{3}$$$$= \pi \times 40 \times 40 \times 24$$$$= 38400\pi \,c{m^3}\,\,\,\,\,\,\,\,\, - - - \left( 1 \right)$$Let the conical vessel is filled in $$x$$ min than length of water column $$=200xm$$So, length of the cylinder $$=2000x\,cm$$and diameter of pipe $$=4cm$$Now,Volume of water flows in $$x$$ minutes $$= \pi \times {\left( {2cm} \right)^2} \times 20000cm$$$$= 8000\pi x\,c{m^3}\,\,\,\,\,\,\,\, - - - - \left( 2 \right)$$Equating $$(1)$$ and $$(2)$$ we get$$38400\pi = 8000\pi x$$$$x=4min\,48sec$$Hence, which is the required answer.Physics

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