Question

500 persons have to dip in a rectangular tank which is 80 m long and 50 m broad. What is the rise in the level of water in the tank, if the average displacement of water by a person is 0.04 m³?​

Answer 1

Answer:

The rise in water level of the rectangular tank is 50 m  = 0.5 cm  

Step-by-step explanation:

Given :  

Number of persons to dip in a rectangular tank = 500  

Length of a rectangular tank (l) = 80 m

Breadth of the rectangular tank (b) = 50 m

Average displacement of water by 1 person = 0.04 m³

Volume of water displaced by 500 persons = 500 × 0.04 = 20 m³ ………….(1)

Let ‘h’ m  be the height of the raised water .

Volume of the rectangular tank = length × breadth ×  height = lbh

= 80 × 50 × h m³ = 4000h m…… ……….(2)

Volume of the raised water in the rectangular tank  is equal to  the volume of water displaced by 500 persons.

Volume of the rectangular tank = Volume of water displaced by 500 persons  

4000h = 20 m³

[From eq 1 & 2]  

h = 20/4000 = 1/200 = 0.005 m  = 0.5 cm  

h = 0.005 m  = 0.5 cm  

Hence, The rise in water level of the rectangular tank is 0.005 m  = 0.5 cm  

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Answer 2

$\textbf{\huge\underline{\underline\red{solution} : - }} \\ \\ \bold{\underline\purple{here \: we \: know}} \\ \\ \red{1.} \bold \blue{ \: length \: (l)\: of \: rectangle \: \: tank \: is \: 80 \: m .} \\ \red{2.} \bold \blue{ \: breadth \:( b)\: of \: rectangle \: tank \: is \: 50 \: m.} \\ \red{3.} \bold \blue{ \: displacement \: of \: water \: by \: a \: one \: } \\ \bold \blue{person \: in \: a \: tank \: is \: 0.04 \: {m}^{3} .} \\ \\ \underline \bold\red{so \: \:displacement \: of \: water \: in \: a \: tank \: by \:} \\ \underline \bold\red{ 500 \: persons } = \blue{500 \times 0.04 = 20 \: }\bold\blue{ {m}^{3} \: \: \: \: ..(1)} \\ \\ \underline \bold \purple{let \: height \: of \: rectangular \: tank \: is \: h} \\ \\ \underline\bold\blue{to \: find \: volume \: of \: water \: in \: tank} \\ \\ \underline \bold \red{volume\: of \: rectangular \: tank \: } = \bold \purple{ l\times b\times h} \\ \\ \bold \red{v.o.r.t} = \bold \purple{80 \times 50 \times h} \\ \\ \bold \red{v.o.r.t} = \bold \purple{(4000 \times h \: \: ) {m}^{3} \: \: \: ..(2) } \\ \\ \underline\bold\blue{as \: we\: know} \\ \\ \underline\bold\purple{volume \: of \: raised \: water \: in \: rectangular } \\ \underline\bold\purple{tank \: is \: equal \: to \: displacement \: of \: water \: in } \\ \underline\bold\purple{ tank\: by \:500 \: person .} \\ \\ \underline\bold\red{hence} \\ \\ \bold\red{volume \: of \: raised \: water \: in \: rectangular } \\\bold\red{tank \:} = \bold\purple{ displacement \: of \: water \: in } \\ \bold\purple{ tank\: by \:500 \: person .} \\ \\ = > \bold \blue{4000 \times h} = \bold \blue{20} \\ \\ = > \bold \blue{h} = \bold \blue{ \frac{2 0}{4000}} = \bold \blue{ \frac{1}{200} } = \bold \blue{0.005 \: m} \\ \\ \underline \bold\red{Hence \: \purple{0.005 \: m} \: level \: of \: water \: rise \: in \: tank.}$