Question

Water flows at the rate of 15 km/hr through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide . In what time will the level of water in the pond rise by 21 cm.  

Answer 1

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

Speed of water = 15 km/hr = 15000 m/hr

\[\text { Diameter of the pipe }= 14 cm = \frac{14}{100}m\]

\[\text { So, the radius of the pipe, r } = \frac{14}{2 \times 100} = \frac{7}{100}m\]

Volume of water flowing out of the pipe in 1 hour

\[= \pi r^2 h\]

\[ = \pi \times \left( \frac{7}{100} \right)^2 \times 15000 m^3 \]

\[ = 231 m^3\]

∴ Volume of water flowing out of the pipe in t hours = 231t m³.

Volume of water in the cuboidal pond

\[= 50 m \times 44 m \times \frac{21}{100} m\]

\[ = 462 m^3\]

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

∴ 231t = 462

        `t = 462 /231`

       ` t = 2`

Thus, the water in the pond rise by 21 cm in 2 hours.