A rectangular sump has an inner length and breadth of $24 m$ and $20 m$ respectively Water flows through an inlet pipe at $180 m$ per minute The cross - sectional area of the pipe is $0.5 m^{2}$ . The tank takes half an hour to get filled. Find the depth of the sump (in $m$ )

4.75

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4.825

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5.625

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5.78

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Solution

The correct option is B $5.625$
In one minute, if $180 m$ of water is flown, then in half hour, length or distance covered by the water $= 180 \times 30 = 5400 m$
Since the pipe is cylindrical in shape, Volume $= A r e a o f c r o s s - s e c t i o n \times h e i g h t$
Here, height is considered as the distance travelled.
Hence, Volume of water which flows in half an hour $= 0.5 \times 5400 m^{3} = 2700 m^{3}$
Now, this $2700 m^{3}$ of water will fill the cuboidal sum to a height say "h".
=> Volume of the tank till height $h = 2700 m^{3}$
$=> l e n g t h \times b r e a d t h \times h = 2700$
$=> 24 \times 20 \times h = 2700$
$=> h = 5.625 m$

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A rectangular sump has an inner length and breadth of 24m and 20m respectively Water flows through an inlet pipe at 180m per minute The cross - sectional area of the pipe is 0.5m2. The tank takes half an hour to get filled. Find the depth of the sump (in m)

A rectangular sump has an inner length and breadth of $24 m$ and $20 m$ respectively Water flows through an inlet pipe at $180 m$ per minute The cross - sectional area of the pipe is $0.5 m^{2}$ . The tank takes half an hour to get filled. Find the depth of the sump (in $m$ )