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Question

Water flows at the rate of $$10$$m per minute through a cylindrical pipe $$5$$ mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is $$40$$cm and depth $$24$$cm?


Solution

R.E.F image 
Volume of cone $$ = \dfrac{1}{3}\times r^{2}h $$

$$ = \dfrac{1}{3}\times 3.14\times 20\times 20\times 24 $$ 

$$ = 3.14\times 400\times 8 $$ 

$$ = 10048\, cm^{3} $$

Volume flown in $$1$$ min $$ = \pi r^{2}h $$

$$ = 3.14\times \dfrac{2.5}{10}\times \dfrac{2.5}{10}\times 1000\, cm^{3} $$

$$ = 196.25\, cm^{3} $$

$$ \therefore $$ time taken $$ = \dfrac{10048}{196.25} = 51.2 $$

$$ \therefore $$ 51 minutes and 2 seconds 

Mathematics

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