Question

water flow out through a circular pipe whose internal diameter is 2 cm at the rate of 6 m per second into cylindrical tank the radius of whose base is 60 cm find the rise in level of water in 30 minutes

Answer 1

The answer is 300 cm

Answer 2

$Internal \: diameter \: of \: the \: pipe$

$So, its \: radius = 1cm = \frac{1}{100}$

$\begin{gathered}Water \: that \: flows \: out \: through \: the \\ pipe \: in \: 6ms {}^{ - 1} \\ so \: volume \: of \: water \: that \: flows \: out \: \\ through \: the \: pipe \: in \: \\ 1sec \: = \pi \times \frac{1 {}^{2} }{100} \times 6m {}^{3} \end{gathered}$

$\begin{gathered}∴ In \: 30 \: minutes,volume \: of \: water \: \\ flow = \pi \frac{1}{100 \times 100} \times 6 \times 30 \times 60m {}^{3} \end{gathered}$

This must be equal to the volume of water that rises in the cylindrical tank after 30 minutes and height up to which it rises say h.

$Radius \: of \: tank = 60cm = \frac{60}{100}$

$Volume \: = \pi( \frac{60}{100} ) {}^{2}$

$= > \frac{60 \times 60}{100 \times 100} h = \frac{60 \times 30 \times 60}{100 \times 100}$

$= > h = \frac{3 \times 36}{36} = 3m$

$\fbox\red{So,required height will be 3m}$