Question

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. if the average displacement of water by a man is 4 m3, then write down the rise in the water level in the tank. show working.

Answer 1

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Answer 2

$\textbf{\huge\underline{\underline\red{solution} : - }} \\ \\ \bold{\underline\purple{here \: we \: know}} \\ \\ \red{1.} \bold \blue{ \: length \: (l)\: of \: rectangle \: \: tank \: is \: 40 \: m .} \\ \red{2.} \bold \blue{ \: breadth \:( b)\: of \: rectangle \: tank \: is \: 20 \: m.} \\ \red{3.} \bold \blue{ \: displacement \: of \: water \: by \: a \: one \: } \\ \bold \blue{person \: in \: a \: tank \: is \: 4 \: {m}^{3} .} \\ \\ \underline \bold\red{so \: \:displacement \: of \: water \: in \: a \: tank \: by \:} \\ \underline \bold\red{ 50 \: persons } = \blue{50 \times 4 = 200 \: }\bold\blue{ {m}^{3} \: \: \: \: ..(1)} \\ \\ \underline \bold \purple{let \: height \: of \: rectangular \: tank \: is \: h} \\ \\ \underline\bold\blue{to \: find \: volume \: of \: water \: in \: tank} \\ \\ \underline \bold \red{volume\: of \: rectangular \: tank \: } = \bold \purple{ l\times b\times h} \\ \\ \bold \red{v.o.r.t} = \bold \purple{40 \times 20 \times h} \\ \\ \bold \red{v.o.r.t} = \bold \purple{(800 \times h \: \: ) {m}^{3} \: \: \: ..(2) } \\ \\ \underline\bold\blue{as \: we\: know} \\ \\ \underline\bold\purple{volume \: of \: raised \: water \: in \: rectangular } \\ \underline\bold\purple{tank \: is \: equal \: to \: displacement \: of \: water \: in } \\ \underline\bold\purple{ tank\: by \:50 \: person .} \\ \\ \underline\bold\red{hence} \\ \\ \bold\red{volume \: of \: raised \: water \: in \: rectangular } \\\bold\red{tank \:} = \bold\purple{ displacement \: of \: water \: in } \\ \bold\purple{ tank\: by \:50 \: person .} \\ \\ = > \bold \blue{800 \times h} = \bold \blue{200} \\ \\ = > \bold \blue{h} = \bold \blue{ \frac{200}{800}} = \bold \blue{ \frac{1}{4} } = \bold \blue{0.25 \: m} \\ \\ \underline \bold\red{Hence \: \purple{0.25 \: m} \: level \: of \: water \: rise \: in \: tank.}$