Question

Water flows out through a circular pipe whose internal diameter is $2cm$, at the rate of $6$ metres per second into a cylindrical tank. The radius of whose base is $60cm$. The rise in the level of water in $30$ minutes is

• A. $3m$
• B. $-3m$
• C. $6m$
• D. $-6m$

Answer 1

The correct option is A $3m$

Internal diameter of the pipe $=2cm$
So its radius $=1cm=\frac{1}{100}m$
Water that flows out through the pipe in $6m{s}^{-1}$
So volume of water that flows out through the pipe in $1sec=\pi \times {\frac{1}{100}}^2\times 6m^3$
$\therefore$ In 30 minutes, volume of water flow $=\pi \frac{1}{100\times 100}\times 6\times 30\times 60m^3$
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 $=60cm=\frac{60}{100}m$
Volume $=\pi {\left(\frac{60}{100}\right)}^{2}h$
$=\pi {\left(\frac{60}{100}\right)}^{2}h=\pi \times \frac{1}{100\times 100}\times 6\times 30\times 60$
$\Rightarrow \frac{60\times 60}{100\times 100}h=\frac{6\times 30\times 60}{100\times 100}$
$\Rightarrow h=\frac{3\times 36}{36}=3m$
So required height will be $3m$.