Question

Water flows at the rate of $5km/hr$ through a pipe of diameter $14cm$ into a rectangle tank which is $25m$ long and $22m$ wide. Find the time in which the level of water in the tank rises by $21cm$. $(Take\pi =\frac{22}{7})$

• A. $2hrs$
• B. $5hrs$
• C. $3hrs$
• D. $1.5hr$

Answer 1

Answer: (D)

$1.5hr$

Diameter of pipe $=14$cm, Water speed $=5\frac{km}{hr}$

Let in ${}^{\prime }{t}^{\prime }$ hours, the level of water rises by $21cm$.

Volume of water flowing out of the pipe in $1$ hour $=$ $\pi r^2\times 5000$

$=\frac{22}{7}\times \frac{7}{100}\times \frac{7}{100}\times 5000$

$=77$$m^3$

$\therefore$ Volume of water flowing out of the pipe in ${}^{\prime }{t}^{\prime }$ hours $=77t$$m^3$

Volume of water in tank $=25\times 22\times \frac{21}{100}=115.5m^3$

Now, Volume of water flowing out $=$ Volume of water in tank

$\Rightarrow 77t=115.5\Rightarrow t=\frac{115.5}{77}=1.5hr$