Question

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

• A. $2m$
• B. $3m$
• C. $4m$
• D. $5m$

Answer 1

The correct option is B $3m$

Length of water flown in $30$ minutes

$=(6\times 60\times 30)=10800$ m

Radius of pipe $=\frac{1}{100}m,h=10800m$

$\therefore$ Volume of water flown through the pipe

$=(\pi \times \frac{1}{100}\times \frac{1}{100}\times 10800)m^3$

Let $h$ be the rise in the level of water in the tank in 30 minutes.

Then, $\pi \times \frac{60}{100}\times \frac{60}{100}\times h=\pi \times \frac{1}{100}\times \frac{1}{100}\times 10800$

$\Rightarrow h=\frac{108}{100}\times \frac{5}{3}\times \frac{5}{3}=3m.$