Question

Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time (in hours) will the level of water in pond rise by 21 cm?

Answer 1

Given that,

Water is flowing at the rate of $15kmph$ through a pipe of diameter $14cm$.

The length of the cuboidal pond is $50m$ and its width is $44m$.

To find out,

How much time will it take in hours for the level of water to raise to $21cm$ height.

Volume of water that comes out of the cylindrical pipe in one hour will be equal to the volume of a cylinder having diameter $14cm$ and height $15km$.

We know that, volume of a cylinder $=\pi r^{2}h$

Here, $r=\frac{14}{2}=7cm$ and $h=15km$

Using the relations $1m=100cm$ and $1km=1000m$, we get:

$r=0.07m$ and $h=15000m$

Hence, volume of water in one hour $=\frac{22}{7}\times (0.07{)}^2\times 15000[\because \pi =\frac{22}{7}]$

$=\frac{1617}{7}{m}^3$

$=231m^3$

Also, volume of water in the pond at the height of $21cm$ will be the volume of a cuboid having length $50m$, width $44m$ and height $21cm$.

We know that, volume of a cuboid $=l\times b\times h$

Here, $l=50m,b=44m$ and $h=0.21m$

Hence, volume of water in the pond at the height of $21cm=50\times 44\times 0.21$

$=462m^3$

Now, the time taken by the pipe to fill the pond to the height of $21cm=\frac{\text{Volume of water in the pond till 21 cm height}}{\text{Volume of water discharged by the pipe in one hour}}$

Hence, time $=\frac{462}{231}$

$=2hours$

Hence, in $2hours$ the water level in the pond will rise to a height of $21cm$.