Question

Water in a cylindrical tank of a diameter $4m$ and height $10m$ is released through a cylindrical pipe of diameter $10cm$ at the rate of $2.5Km/hr$. How much time will it take to empty the half of the tank? Assume that the tank is full of water to begin with.

• A. $3hr$ $12min$
• B. $2hr$ $12min$
• C. $3hr$ $22min$
• D. None of these

Answer 1

The correct option is A $3hr$ $12min$

Let us convert every measurements into m

Diameter of the cylindrical tank $=4$m

Radius of the cylindrical tank $=\frac{4}{2}=2$ m

Height of the tank $=10$ m

Diameter of the cylindrical pipe $=10$cm

Radius of the cylindrical pipe $=\frac{10}{2}=5$cm

$1$m$=100$cm

$5$cm$=\frac{5}{100}$m

speed of water $=2.5$ km/hr

We know that $1000$m$=1$ km

$=2.5\times 1000$m\hr

$=2500$ m/hr

Volume of water discharged from the cylindrical pipe $=\frac{1}{2}\times$ Volume of cylindrical tank

Area of cross section $\times$time$\times$speed$=\frac{1}{2}\pi r^{2}h$

$\pi r^2\times$time$\times$speed$=\frac{1}{2}\pi r^{2}h$

${\left(\frac{5}{100}\right)}^2\times$ Time $\times 2500=\frac{1}{2}\times 2^2\times 10$

$\frac{5}{100}\times \frac{5}{100}\times$ Time$\times 2500=\frac{1}{2}\times 4\times 10$

Time $=2\times 10\times \frac{100}{5}\times \frac{100}{5}\times \frac{1}{2500}$

Time$=\frac{80}{25}$ on evaluation

$=3.2$ hour

We know that $1$ hour$=60$ minute

$192$ minute$=180+12$

$=3$ hour and $12$ minute

$\therefore$ time taken to empty the half of the tank is $3$ hour and $12$ minute