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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 have
Diameter 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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