Filling a tank

Geometry Level 2

Water is flowing at the rate of 5 km/hr through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Determine the time(in hours) in which the level of the water in the tank will rise by 7 cm.

Take π = 22 7 \pi =\frac { 22 }{ 7 }

2.5 2 3 1.5

Krishna Ramesh by Krishna Ramesh , 22, India

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1 solution

Krishna Ramesh
May 12, 2014

Let the time taken be x hours.

length of water column in x hours = 5000x m

so, volume of water flowing in pipe in x hours = π r 2 h \pi { r }^{ 2 }h

= 22 7 × ( 7 100 ) 2 × 5000 x = 77 x m 3 =\frac { 22 }{ 7 } \times { \left( \frac { 7 }{ 100 } \right) }^{ 2 }\times 5000x=\quad 77x\quad { m }^{ 3 }

now, required volume of water in tank= 50 × 44 × ( 7 100 ) = 154 m 3 50\times 44\times \left( \frac { 7 }{ 100 } \right) =154\quad { m }^{ 3 }

so, 77 x = 154 ⇒ x = 2 77x=154\quad \Rightarrow \quad x=\boxed{2}

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