A social welfare association decides to supply water for flood affected people. The drinking Water is filled in a water tanker which is in shape of cylinder with hemispherical ends. whole length is 4.2 m n diameter of base of cylinder an2 hemisphere each 12 m they distribute water to 60 people in container shapre of cylinder of radius 21cm n height 50 cm find quantity of water left in tanker after distribution in litres
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Answer:
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Step 1:
The length of the water tank = 4.2 m
The diameter of the base of the cylinder and the two hemispherical ends,
d = 1.2 m
So, the radius, r = d/2 = 1.2/2 = 0.6 m
∴ The length of the cylindrical portion of the tank, h = 4.2 - 1.2 = 3 m
Now,
The volume of the cylindrical portion is,
= πr²h
= × 0.6² × 3
= 3.39 m³
and
The volume of the 2 hemispherical ends is,
= 2 × [ πr³]
= × × 0.6³
= 0.905 m³
∴ The volume of the drinking water tank is given by,
= [ volume of the cylindrical portion] + [volume of the 2 hemispherical ends]
= 3.39 m³ + 0.905 m³
= 4.295 m³
Step 2:
The dimension of the small cylindrical containers:
Radius, r = 21 cm = 0.21 m
Height, h = 50 cm = 0.5 m
The no. of people to whom the drinking water was distributed in cylindrical containers = 60
∴ The volume of water distributed to 60 people is given by,
= 60 * [Volume of the cylindrical containers]
= 60 * [πr²h]
= 60 * (22/7) * 0.21² * 0.5
= 4.158 m³
Step 3:
Therefore,
The quantity of water left in the tanker after the distribution is given by,
= [volume of the drinking water tank] – [volume of water distributed to 60 people]
= 4.295 m³ - 4.158 m³
= 0.137 m³
∵ 1 m³ = 1000 litres
= 137 litres