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  4. 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).

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Q. 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).

Mensuration

Solution:

Let the depth of the sump be $h m$.
Volume of water flowing through the pipe $=(180)$
$(0.5) m ^3 /$ minute $=90\, m ^3 /$ minute.
Total volume of water which must flow through to fill the sump $=(90)(30)=2700 cm ^3$.
$\therefore(24)(20)(h)=2700$
$h=5.625$.