Water is flowing at the rate of $15\ km/h$ through a pipe of diameter of $14\ cm$ into a cuboidal pond which is $50\ m$ long ang $44\ m$ wide. In what time will the level of water in the pond rise by $22\ cm$?

Academic Mathematics NCERT Class 10

Given: Water is flowing at the rate of $15\ km/h$ through a pipe of diameter of $14\ cm$ into a cuboidal pond which is $50\ m$ long ang $44\ m$ wide

To do: To find the time for the level of water in the pond rise by $22\ cm$.

Solution:

Let the level of water in the pond rises by $21\ cm$ in $t$ hours.

Speed of water $=15\ km/hr$

Diameter of the pipe$= \frac{14}{100}\ m$

Radius of the pipe $( r) = \frac{7}{100}\ m$

Volume of water flowing out of the pipe in 1 hour

$=\pi r^{2}h$

$= ( \frac{22}{7})\times( \frac{7}{100})\times( \frac{7}{100})\times15000$

$= 231\ m^{3}$

Volume of water flowing out of the pipe in $t$ hours $=231t\ m^{3}$

Volume of water in the cuboidal pond

$= 50 \times 44 \times ( \frac{21}{100})$

$= 462\ m^{3}$

Volume of water flowing out of the pipe in $t$ hours $=$ Volume of water in the cuboidal pond

So, $231t = 462$

$\Rightarrow t = \frac{462}{231}=2$

Thus, the required time is $2$ hours.

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Updated on: 10-Oct-2022

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