Math, asked by jyothizeejyothizee, 10 months ago

the whole length of the tank is 4.2 metre and the diameter of the base of the cylinder and two hemispheres are each 1.2 metre if there distribute drinking water to 60 people in a container each is in the shape of a cylinder of radius 21 cm and height 50 cm find the quantity of water left in the tanker after distribution in litre ( use π= 22/7)

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Answered by Anonymous

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$given \: that \\ total \: height \: of \: the \: tank(h) = 4.2m= 420cm \\ diameter \: of \: cylinder = 1.2m= 120cm \\ radius \: of \: the \: cylinder = 0.6m= 60cm \\ volume \: of \: the \: tank = volume \: of \: cylinder + 2 \times volume \: of \: hemisphere$

$= \pi \: r {}^{2} h + 2 \times 2 \div 3\pi \: r {}^{3} \\ = \pi \: r {}^{2} h + 4 \div 3\pi \: r {}^{3} \\ = 22 \div 7 \times (0.6 ) {}^{2} \times 3 + 4 \div 3 \times 22 \div 7 \times (0.6) {}^{3} \\ = 3.3942 + 0.9051 \\ = 4.2993m {}^{3}$

$radius \: of \: container(r1) = 0.21m= 21cm \\ height \: of \: the \: container(h1) = 0.5m = 50cm \\ volume \: of \: 1st \: container = \pi \: (r1) {}^{2} h1 \\$

$= 22 \div 7 \times (0.21) {}^{2} \times 0.5 = 0.0693 \\ volume \: of \:60 \: containers = 60 \times 0.0693 \\ = 4.158 m{}^{3} \\ quantity \: of \: water \: left \: in \: the \: tank = volume \: of \: tank - volume \: of \: 60\: containers \\ 0.1413m {}^{3}$

$wkt. \: 1m {}^{3} = 1000litres \\ quantity \: of \: water \: left \: in \: the \: tank = 141.3litres \\ hight \: of \: the \: cylinder(h) = total \: height - 2 \times radius \: of \: hemisphere \\ = 4.2 - 1.2 \\ = 3m = > 300cm$

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