Question

Water flows in a tank $150\text{ }m\times 100\text{ }m$ at the base through a pipe whose cross-section is $2\text{ }dm\times 1\cdot 5\text{ }dm$ at the speed of $15km/hr.$ In what time, will the water be $3m$ deep?

Answer 1

Hint: We have to find the volume required in the tank by using the formula of volume of cuboid and volume of water flowing through the pipe. In order to find the time required to fill the tank through the pipe. We should divide the volume of the tank with the volume of water passing through the pipe.

Formula Used:
 \[\text{Volume of Cuboid }\!\!~\!\!\text{ }=l\times b\times h\]
\[\text{Volume of water through pipe}\]\[=2\text{ }dm\times \text{1}\cdot \text{5 }dm\times 15km/hr\]
Time= Volume of water in tank required/ Volume of water passing through pipe per hour

Complete step-by-step answer:

$\begin{align}
  & \text{Length of tank}=150\text{ }m\text{ (L)} \\
 & \text{Width of tank}=100\text{ }m\text{ (b)} \\
 & \text{Want to fill tank to }3\text{ }m\text{ depth} \\
 & \therefore \text{Height of tank}=3\text{ }m\text{ (h)} \\
\end{align}$
$\begin{align}
  & \text{Volume of tank}=l\times b\times h \\
 & \text{ }=150\times 100\times 3 \\
 & \text{ }=45000\text{ }{{m}^{3}} \\
\end{align}$
Water is passing through pipe having a cross-section is \[2\text{ }dm\times \text{1}\cdot \text{5 }dm\] and water is flowing $15km/hr$
\[2\text{ }dm=2\times {{10}^{-1m}}\text{ }\!\!\And\!\!\text{ 1}\cdot \text{5}\times \text{1}{{\text{0}}^{-1}}\text{ }15km/hr=15000\text{ }m/hr\]
Therefore
Rate of volume of water through pipe\[=2\times {{10}^{-1}}\times \text{1}\cdot \text{5}\times {{10}^{-1}}\times 5000\text{ }{{m}^{3}}/hr\]
 \[=450{{m}^{3}}/hr\]
Time Taken = Volume of tank/Rate of flow of water through pipe
\[\begin{align}
  & =\frac{45000}{450}hr \\
 & \text{=100hr} \\
\end{align}\]

Additional information:
 Students can solve this question to reduce the calculation.
Time= Volume of tank/ Volume of water through pipe.
Time=\[150\times 100\times 3/2\times {{10}^{-1}}\times 1\cdot 5\times {{10}^{-1}}\times 15000\]
$=150\times 100\times 3/2\times {{10}^{-1}}\times 1\cdot 5\times {{10}^{-1}}\times 15000$
 $=3\times 10\times 10\times 10/2\times 15$
 $=100\text{hrs}$

Note: Time taken = Volume to be filled in tank/ volume passes through pipe per hour.
So the answer will be hours because rest is cancelled.