Question

Water flows at the rate of 5 m per min from a cylindrical pipe 8 mm in diameter. how long will it take to fill up a conical vessel whose radius is 12 cm and depth 35 cm?

Answer 1

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Answer 2

$Given \: diameter \:of \:the \: pipe = 8\: mm$

$Radius \: of \:the \:pipe =\frac{diameter }{2} \\= 4 \:mm \\= \frac{4}{10} \: cm \\= \frac{2}{5} \:cm$

$Speed \: of \:water = 5 \: m /min \\= 500 \: cm /min$

$Volume \:of \:water \:that \: flows \: in \:1 \:min\\= \pi r^{2} h \\= \frac{22}{7} \times \frac{2}{5} \times \frac{2}{5} \times 500 \\= \frac{1760}{7} \:cm^{3} \: --(1)$

$Radius \:of \: conical \:vessel = 12 \:cm$

$Depth = 35 \:cm$

$\therefore Capacity \:of \:the \: vessel \\= \frac{1}{3} \times \pi r^{2} h$

$= \frac{1}{3} \times \frac{22}{7}\times 12 \times 12 \times 36 \\= \frac{38016}{7} \:cm^{3} \:--(2)$

$Time \: required \:to \:fill \: the \: vessel \\=\frac{ capacity \: of \: the \:vessel }{Volume \:of \: water \:flowing \:per \:minute } \\= \frac{ \frac{38016}{7}}{\frac{1760}{7}}\\= \frac{38016}{1760} \\= 21\frac{3}{5} \:min$

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